COVID-19 information for PI Residents and Visitors
Perimeter Institute has launched a new program whereby child care support may be available to facilitate your participation in workshops and conferences. Please visit http://www.perimeterinstitute.ca/research/conferences/child-care-support-conference-participants for more information.
- Bartek Czech, Institue for Advanced Study
- Glen Evenbly, University of Sherbrooke
- Martin Ganahl, Perimeter Institute
- Jutho Haegeman, University of Ghent
- Janet Hung, Fudan University
- Robert Leigh, University of Illinois at Urbana-Champaign
- Ashley Milsted, Perimeter Institute
- Robert Myers, Perimeter Institute
- *Tobias Osborne, University of Hannover
- Xiaoliang Qi, Stanford University
- Volker Scholz, Ghent University
- Miles Stoudenmire, University of Calfornia, Irvine
- Jamie Sully, McGill University
- Brian Swingle, MIT, Harvard University & Brandeis University
- Tadashi Takayanagi, Yukawa Institute for Theoretical Physics
- Frank Verstraete, University of Ghent
- Guifre Vidal, Perimeter Institute
- Steven White, University of California, Irvine
*via teleconference
- Javier Arguello, Perimeter Institute
- Ganapathy Baskaran, Institute of Mathematical Sciences Chennai
- Lakshya Bhardwaj, Perimeter Institute
- Arpan Bhattacharyya, Fudan University
- Dean Carmi, Perimeter Institute
- Shira Chapman, Perimeter Institute
- Jordan Cotler, Stanford University
- Bartek Czech, Institute for Advanced Study
- Clement Delcamp, Perimeter Institute
- Bianca Dittrich, Perimeter Institute
- Glen Evenbly, University of Sherbrooke
- Matthew Fishman, California Institute of Technology
- Adrian Franco Rubio, Perimeter Institute
- Adil Gangat, National Taiwan University
- Martin Ganahl, Perimeter Institute
- Jutho Haegeman, University of Ghent
- Muxin Han, Florida Atlantic University
- Markus Hauru, Perimeter Institute
- Joshuah Heath, Boston College
- Michal Heller, Albert Einstein Institute
- Qi Hu, Perimeter Institute
- Janet Hung, Fudan University
- Nick Hunter-Jones, California Institute of Technology
- Robert Jefferson, Perimeter Institute
- Robert Leigh, University of Illinois at Urbana-Champaign
- Adam Lewis, Perimeter Institute
- Shengqiao Luo, Perimeter Institute
- Hugo Marrochio, Perimeter Institute
- Alex May, University of British Columbia
- Roger Melko, Perimeter Institute & University of Waterloo
- Ashley Milsted, Perimeter Institute
- Sebastian Mizera, Perimeter Institute
- Robert Myers, Perimeter Institute
- Xiaoliang Qi, Stanford University
- Jason Pye, University of Waterloo
- Hammam Qassim, Institute for Quantum Computing
- Djordje Radicevic, Perimeter Institute
- Julian Rincon, Perimeter Institute
- Burak Sahinoglu, California Institute of Technology
- Volker Scholz, Ghent University
- Didina Serban, Perimeter Institute
- Andrei Shieber, Perimeter Institute
- Vasudev Shyam, Perimeter Institute
- Joan Simon, University of Edinburgh
- Kevin Slagle, University of Toronto
- Barbara Soda, Perimeter Institute
- Miles Stoudenmire, University of Calfornia, Irvine
- Jamie Sully, McGill University
- Brian Swingle, MIT, Harvard University & Brandeis University
- Tadashi Takayanagi, Yukawa Institute for Theoretical Physics
- Nick Van den Broeck, Perimeter Institute
- Guillaume Verdon-Akzam, Institute for Quantum Computing
- Frank Verstraete, University of Ghent
- Guifre Vidal, Perimeter Institute
- Steven White, University of California, Irvine
- Gabriel Wong, University of Virginia
- Shuo Yang, Perimeter Institute
- Beni Yoshida, Perimeter Institute
- Jose Zapata, Centro de Ciencias Matematicas
- Yijian Zou, Perimeter Institute
Tuesday, April 18, 2017
Time |
Event |
Location |
9:00 – 9:30am |
Registration |
Reception |
9:30 – 9:35am |
Guifre Vidal, Perimeter Institute |
Bob Room |
9:35 – 10:35am |
Steven White, University of California |
Bob Room |
10:35 – 11:00am |
Coffee Break |
Bistro – 1st Floor |
11:00-12:00pm |
Ashley Milsted, Perimeter Institute |
Bob Room |
12:00 – 2:00pm |
Lunch |
Bistro – 2nd Floor |
2:00 – 2:40pm |
Miles Stoudenmire, University of California |
Bob Room |
2:40 – 3:20pm |
Martin Ganahl, Perimeter Institute |
Bob Room |
3:20 – 3:50pm |
Coffee Break |
Bistro – 1st Floor |
3:50 – 4:30 pm |
Jutho Haegeman, University of Ghent |
Bob Room |
Wednesday, April 19, 2017
Time |
Event |
Location |
9:30 – 10:30am |
Guifre Vidal, Perimeter Institute |
Bob Room |
10:30 – 11:00am |
Coffee Break |
Bistro – 1st Floor |
11:00-12:00pm |
Robert Leigh, University of Illinois at Urbana-Champaign |
Bob Room |
12:00 – 2:00pm |
Lunch |
Bistro – 2nd Floor |
2:00 – 2:40pm |
Brian Swingle, |
Bob Room |
2:40 – 3:20pm |
Volkher Scholz, University of Ghent |
|
3:20 – 3:50pm |
Coffee Break |
Bistro – 1st Floor |
3:50 - 4:50pm |
Frank Verstraete, University of Ghent |
Bob Room |
5:00 – 6:00pm |
Poster Session |
Atrium |
6:00pm |
Banquet |
Bistro – 2nd Floor |
Thursday, April 20, 2017
Time |
Event |
Location |
9:30 – 10:30am |
Jamie Sully, McGill University |
Bob Room |
10:30 – 11:00am |
Coffee Break |
Bistro – 1st Floor |
11:00-12:00pm |
Tadashi Takayanagi, Yukawa Institute for Theoretical Physics |
Bob Room |
12:00 – 2:00pm |
Lunch |
Bistro – 2nd Floor |
2:00 – 3:00pm |
Robert Myers, Perimeter Institute |
Bob Room |
3:00 – 3:30pm |
Coffee Break |
Bistro – 1st Floor |
3:30 – 4:10pm |
Bartek Czech, Institute for Advanced Study |
Bob Room |
Friday, April 21, 2017
Time |
Event |
Location |
9:00 – 10:00am |
Xiaoliang Qi, Stanford University |
Bob Room |
10:00 – 10:30am |
Coffee Break |
Bistro – 1st Floor |
10:30 – 11:10am |
Tobias Osborne, University of Hannover [via teleconference] |
Bob Room |
11:10 – 11:50am |
Janet Hung, Fudan University |
Bob Room |
11:50 – 12:30pm |
Glen Evenbly, University of Sherbrooke |
Bob Room |
12:30pm |
Lunch |
Bistro – 2nd Floor |
Bartek Czech, Institute for Advanced Study
How Tensor Network Renormalization quantifies circuit complexity and why this is a problem of [considerable] gravity
According to a recent proposal, in the AdS/CFT correspondence the circuit complexity of a CFT state is dual to the Einstein-Hilbert action of a certain region in the dual space-time. If the proposal is correct, it should be possible to derive Einstein's equations by varying the complexity in a class of circuits that prepare the requisite CFT state. This talk attempts such a derivation in very special settings: Virasoro descendants of the CFT2 ground state, which are dual to locally AdS3 geometries. By applying Tensor Network Renormalization to the discretized Euclidean path integral that prepares the CFT state, I will justify the recent suggestion by Caputa et al. that the complexity of a path integral is quantified by the Liouville action. The Liouville field specifies the conformal frame in which the path integral is evaluated; in the most efficient / least complexity frame, the Liouville field is closely related to entanglement entropies of CFT2 intervals. Assuming the Ryu-Takayanagi proposal, the said entanglement entropies are lengths of geodesics living in the dual space-time. The Liouville equation of motion satisfied by the minimal complexity Liouville field is a geodesic-wise rewriting of the non-linear vacuum Einstein's equations in 3d with a negative cosmological constant. I emphasize that this is very much work in progress; I hope the audience will help me to sharpen the arguments.
Glen Evenbly, University of Sherbrooke
Hyper-invariant tensor networks and holography
I will propose a new class of tensor network state as a model for the AdS/CFT correspondence and holography. This class shall be demonstrated to retain key features of the multi-scale entanglement renormalization ansatz (MERA), in that they describe quantum states with algebraic correlation functions, have free variational parameters, and are efficiently contractible. Yet, unlike MERA, they are built according to a uniform tiling of hyperbolic space, without inherent directionality or preferred locations in the holographic bulk, and thus circumvent key arguments made against the MERA as a model for AdS/CFT. Novel holographic features of this tensor network class will be examined, such as an equivalence between the causal cone C[R] and the entanglement wedge E[R] of connected boundary regions R.
Martin Ganahl, Perimeter Institute
Solving Non-relativistic Quantum Field Theories with continuous Matrix Product States
Since its proposal in the breakthrough paper [F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 104, 190405(2010)], continuous Matrix Product States (cMPS) have emerged as a powerful tool for obtaining non-perturbative ground state and excited state properties of interacting quantum field theories (QFTs) in (1+1)d. At the heart of the cMPS lies an efficient parametrization of manybody wavefunctionals directly in the continuum, that enables one to obtain ground states of QFTs via imaginary time evolution. In the first part of my talk I will give a general introduction to the cMPS formalism. In the second part, I will then discuss a new method for cMPS optimization, based on energy gradient instead of the usual imaginary time evolution. This new method overcomes several problems associated with imaginary time evolution, and allows to perform calculations at much lower cost / higher accuracy than previously possible.
Jutho Haegeman, University of Ghent
Bridging Perturbative Expansions with Tensor Networks
We demonstrate that perturbative expansions for quantum many-body systems can be rephrased in terms of tensor networks, thereby providing a natural framework for interpolating perturbative expansions across a quantum phase transition. This approach leads to classes of tensor-network states parameterized by few parameters with a clear physical meaning, while still providing excellent variational energies. We also demonstrate how to construct perturbative expansions of the entanglement Hamiltonian, whose eigenvalues form the entanglement spectrum, and how the tensor-network approach gives rise to order parameters for topological phase transitions.
Janet Hung, Fudan University
Tensor network and (p-adic) AdS/CFT
We will describe how the reconstruction of a bulk operator can be organised systematically. With a suitable parametrisation, an analogue of the HKLL formula emerges, involving a smearing function satisfying a Klein Gordon equation in the graph. The parametrisation also allows us to read off interaction vertices, and build up loop diagrams systematically. When we interpret the Bruhat-Tits tree as a tensor network, we recover (partially) features of the p-adic AdS/CFT dictionary discussed recently in the literature.
Robert Leigh, University of Illinois at Urbana-Champaign
Unitary Networks from the Exact Renormalization of Wavefunctionals
The exact renormalization group (ERG) for O(N) vector models at large N on flat Euclidean space admits an interpretation as the bulk dynamics of a holographically dual higher spin gauge theory on AdS_{d+1}. The generating functional of correlation functions of single trace operators is reproduced by the on-shell action of this bulk higher spin theory, which is most simply presented in a first-order (phase space) formalism. This structure arises because of an enormous non-local symmetry of free fixed point theories. In this talk, I will review the ERG construction and describe its extension to the RG flow of the wave functionals of arbitrary states of the O(N) vector model at the free fixed point. One finds that the ERG flow of the ground state and a specific class of excited states is implemented by the action of unitary operators which can be chosen to be local. Thus the ERG equations provide a continuum notion of a tensor network. We compare this tensor network with the entanglement renormalization networks, MERA, and cMERA. The ERG tensor network appears to share the general structure of cMERA but differs in important ways.
Ashley Milsted, Perimeter Institute
Emergence of conformal symmetry in critical spin chains
We demonstrate that 1+1D conformal symmetry emerges in critical spin chains by constructing a lattice ansatz Hn for (certain combinations of) the Virasoro generators Ln. The generators Hn offer a new way of extracting conformal data from the low energy eigenstates of the lattice Hamiltonian on a finite circle. In particular, for each energy eigenstate, we can now identify which Virasoro tower it belongs to, as well as determine whether it is a Virasoro primary or a descendant (and similarly for global conformal towers and global conformal primaries/descendants). The central charge is obtained from a simple ground-state expectation value. Non-universal, finite-size corrections are the main source of error. We propose and demonstrate the use of periodic Matrix Product States, together with an improved ground state solver, to reach larger system sizes. We uncover that, importantly, the MPS single-particle excitation ansatz accurately describes all low energy excited states.
Robert Myers, Perimeter Institute
Complexity, Holography & Quantum Field Theory
I will describe some recent work studying proposals for computational complexity in holographic theories and in quantum field theories. In particular, I will discuss some interesting properties of the new gravitational observables and of complexity in the boundary theory.
Tobias Osborne, University of Hannover
Dynamics for holographic codes
In this talk I discuss the problem of introducing dynamics for holographic codes. To do this it is necessary to take a continuum limit of the holographic code. As I argue, a convenient kinematical continuum limit space is given by Jones’ semicontinuous limit. Dynamics are then furnished by a unitary representation of a discrete analogue of the conformal group known as Thompson’s group T. I will describe these representations in detail in the simplest case of a discrete AdS geometry modelled by trees. Consequences such as the ER=EPR argument are then realised in this setup. Extensions to more general tessellations with a MERA structure are possible, and will be (very) briefly sketched.
Xiaoliang Qi, Stanford University
Random tensor networks and holographic coherent states
Arpan Bhattacharyya, Fudan University
AdS/CFT via Tensor Network : Bulk boundary Reconstruction
We will demonstrate , how to reconstruct bulk operator starting form the local boundary using our model of tensor network which is basically using being build form the perfect tensor plus some small perturbations away form it. We will show that it has the similar features as that of HKLL construction thereby making the connection with the holography (AdS/CFT) concrete. Also we will demonstrate the connection between the linear part of the operator reconstruction and the wavelet transformation. Further we will show that the non linear part of the reconstruction has the possibility of giving the "Geodesic Witten diagram ". At last , we will consider the example of p-adic tree where all these things can be written down explicitly.
Jordan Cotler, Stanford University
cMERA for Interacting Scalar Fields
We upgrade cMERA to a systematic variational ansatz and develop techniques for its application to interacting quantum field theories in arbitrary spacetime dimensions. By establishing a correspondence between the first two terms in the variational expansion and the Gaussian Effective Potential, we can exactly solve for a variational approximation to the cMERA entangler. As examples, we treat scalar ϕ^4 theory and the Gross-Neveu model and extract non-perturbative behavior. We also comment on the connection between generalized squeezed coherent states and more generic entanglers.
Matthew Fishman, California Institute of Technology
Improving the Corner Transfer Matrix Renormalization Group Method with Fixed Points
We present an explicitly translationally invariant version of the Corner Transfer Matrix Renormalization Group (CTMRG) method, which allows us to reformulate the method in terms of a set of fixed point equations. This leads to speedups in the convergence time of the algorithm, particularly for systems near criticality. To show the performance of the algorithm, we present various benchmarks for contracting 2D statistical mechanics models as well as 2D quantum models written as projected entangled pair states (PEPS).
Adrian Franco Rubio, Perimeter Institute
Entanglement structure and UV regularization in cMERA
The continuous multi-scale entanglement renormalization ansatz or cMERA provides a variational ansatz for the ground state of a quantum field theory. Such states come equipped with an intrinsic length scale that acts as an ultraviolet cutoff. We provide evidence for the existence of this cutoff based on the entanglement structure of a particular family of cMERA states, namely Gaussian states optimized for free bosonic and fermionic CFTs. Our findings reflect that short distance entanglement is not fully present in the ansatz states, thus hinting at ultraviolet regularization.
Adil Gangat, National Taiwan University
Steady States of Infinite-Size Dissipative Quantum Chains via Imaginary Time Evolution
Directly in the thermodynamic limit, we show how to combine imaginary and real time evolution of tensor networks to efficiently and accurately find the nonequilibrium steady states (NESS) of one-dimensional dissipative quantum lattices governed by the Lindblad master equation. The imaginary time evolution first bypasses any highly correlated portions of the real-time evolution trajectory by directly converging to the weakly corre- lated subspace of the NESS, after which real time evolution completes the convergence to the NESS with high accuracy. We demonstrate the power of the method with the dissipative transverse field quantum Ising chain. We show that a crossover of an order parameter shown to be smooth in previous finite-size studies remains smooth in the thermodynamic limit.
Markus Hauru, Perimeter Institute
Topological conformal defects with tensor network
Qi Hu, Perimeter Institute
Continuous Multi-scale Entanglement Renormalization Ansatz
The generalization of the multi-scale entanglement renormalization ansatz (MERA) to continuous systems, or cMERA, is a variational ansatz for the ground state of quantum field theories. For a conformal field theory, it can capture the space-time symmetries of the ground state, and we can extract the conformal data from cMERA.
Adam Lewis, Perimeter Institute
Matrix Product State Simulations of Quantum Fields in an Expanding Universe
The matrix product state (MPS) ansatz makes possible computationally-efficient representations of weakly entangled many-body quantum systems with gapped Hamiltonians near their ground states, notably including massive, relativistic quantum fields on the lattice. No Wick rotation is required to apply the time evolution operator, enabling study of time-dependent Hamiltonians. Using free massive scalar field theory on the 1+1 Robertson-Walker metric as a toy example, I present early efforts to exploit this fact to model quantum fields in curved spacetime. We use the ADM formalism to write the appropriate Hamiltonian witnessed by a particular class of normal observers. Possible applications include simulations of gravitational particle production in the presence of interactions, studies of the slicing-dependence of entanglement production, and inclusion of the expectation of the stress-energy tensor as a matter source in a numerical relativity simulation.
Alex May, University of British Columbia
Tensor networks for dynamic spacetimes
Existing tensor network models of holography are limited to representing the geometry of constant time slices of static spacetimes. We study the possibility of describing the geometry of a dynamic spacetime using tensor networks. We find it is necessary to give a new definition of length in the network, and propose a definition based on the mutual information. We show that by associating a set of networks with a single quantum state and making use of the mutual information based definition of length, a network analogue of the maximin formula can be used to calculate the entropy of boundary regions.
Hugo Marrochio, Perimeter Institute
Holographic complexity and related progress towards a cMERA realization
Julian Rincon, Perimeter Institute
Continuous matrix product representations for mixed states
The continuous matrix product states (cMPS) is a powerful variational ansatz for the ground state of interacting quantum field theories in 1+1 spacetime dimensions [F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 104, 190405(2010)]. Here we propose a density matrix generalization of the cMPS, the continuous matrix product density operator (cMPDO), and investigate its suitability to represent thermal states and master equation dynamics. We show the existence of the cMPDO by taking the continuum limit of a lattice MPDO and characterize its mathematical properties. For thermal states of field theories, we find that the cMPDO offers an accurate description of their corresponding density matrix. We argue that these results can also be extended for the case of master equation dynamics.
Yijian Zou, Perimeter Institute
Extracting conformal data with periodic boundary matrix product states
We construct Virasoro generators on a finite critical lattice system with the periodic boundary condition, and use them to identify conformal towers. Ground state and excited states corresponding to scaling operators are found with periodic boundary matrix product states. Scaling dimensions and central charge are estimated with high accuracy from finite size scaling.
Hyper-invariant tensor networks and holography
I will propose a new class of tensor network state as a model for the AdS/CFT correspondence and holography. This class shall be demonstrated to retain key features of the multi-scale entanglement renormalization ansatz (MERA), in that they describe quantum states with algebraic correlation functions, have free variational parameters, and are efficiently contractible.
Tensor network and (p-adic) AdS/CFT
We will describe how the reconstruction of a bulk operator can be organised systematically. With a suitable parametrisation, an analogue of the HKLL formula emerges, involving a smearing function satisfying a Klein Gordon equation in the graph. The parametrisation also allows us to read off interaction vertices, and build up loop diagrams systematically. When we interpret the Bruhat-Tits tree as a tensor network, we recover (partially) features of the p-adic AdS/CFT dictionary discussed recently in the literature.
Dynamics for holographic codes
In this talk I discuss the problem of introducing dynamics for holographic codes. To do this it is necessary to take a continuum limit of the holographic code. As I argue, a convenient kinematical continuum limit space is given by Jones’ semicontinuous limit. Dynamics are then furnished by a unitary representation of a discrete analogue of the conformal group known as Thompson’s group T. I will describe these representations in detail in the simplest case of a discrete AdS geometry modelled by trees. Consequences such as the ER=EPR argument are then realised in this setup.
Random tensor networks and holographic coherent states
Tensor network is a constructive description of many-body quantum entangled states starting from few-body building blocks. Random tensor networks provide useful models that naturally incorporate various important features of holographic duality, such as the Ryu-Takayanagi formula for entropy-area relation, and operator correspondence between bulk and boundary. In this talk I will overview the setup and key properties of random tensor networks, and then discuss how to describe quantum superposition of geometries in this formalism.
How Tensor Network Renormalization quantifies circuit complexity and why this is a problem of [considerable] gravity
According to a recent proposal, in the AdS/CFT correspondence the circuit complexity of a CFT state is dual to the Einstein-Hilbert action of a certain region in the dual space-time. If the proposal is correct, it should be possible to derive Einstein's equations by varying the complexity in a class of circuits that prepare the requisite CFT state. This talk attempts such a derivation in very special settings: Virasoro descendants of the CFT2 ground state, which are dual to locally AdS3 geometries.
Complexity, Holography & Quantum Field Theory
I will describe some recent work studying proposals for computational complexity in holographic theories and in quantum field theories. In particular, I will discuss some interesting properties of the new gravitational observables and of complexity in the boundary theory.
Two Continous Approaches to AdS/Tensor Network duality
In this talk, I would like to discuss how we can realize the correspondence between AdS/CFT and tensor network in quantum field theories (i.e. the continous limit). As the first approach I will discuss a possible connection between continuous MERA and AdS/CFT. Next I will introduce the second approach based on the optimization of Euclidean path-integral, where the strcutures of hyperbolic spaces and entanglement wedges emerge naturally. This second appraoch is closely related to the idea of tensor network renormalization.
Tensor Networks and Holography
Tensor network renormalization and real space Hamiltonian flows
We will review the topic of tensor network renormalization, relate it to real space Hamiltonian flows, and discuss the emergence of matrix product operator algebras as symmetries of the renormalization fixed points.
joint work with Matthias Bal, Michael Marien and Jutho Haegeman
Analytic approaches to tensor networks for field theories
I will discuss analytic approaches to construct tensor network representations of quantum field theories, more specifically conformal field theories in 1+1 dimensions. A key insight is that we should understand how well the tensor network can reproduce the correlation functions of the quantum field theory. Based on this measure of closeness, I will present rigorous results allowing for explicit error bounds which show that both Matrix product states (MPS) as well as the multiscale renormalization Ansatz (MERA) do approximate conformal field theories.
Pages
Scientific Organizers:
- Robert Myers, Perimeter Institute
- Tadashi Takayanagi, Yukawa Institute for Theoretical Physics
- Frank Verstraete, University of Ghent
- Guifre Vidal, Perimeter Institute
- Steven White, University of California, Irvine