Emergence & Entanglement II 2013

Emergence & Entanglement II 2013

Characterizing topological order form a microscopic lattice Hamiltonian

Thursday May 09, 2013
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In this talk I will show how to obtain a detailed characterization of the emergent topological order starting from microscopic Hamiltonian on a two dimensional lattice. A key step is to obtain a tensor network representation for a complete set of ground states of the Hamiltonian, ﬁrst on an inﬁnite cylinder and then on a ﬁnite torus. As an application of the method I will study lattice Hamiltonians that give rise to selected anyon models, namely chiral semion, Ising as well as Z_3 and Z_5 models.

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Directed Influence in the RG Flow

Thursday May 09, 2013
Speaker(s):

Given two lattice Hamiltonians H_1 and H_2 that are identical everywhere except on a local region R of the lattice, we propose a relationship between their ground states psi_1 and psi_2.  Specifically, assuming the states can be represented as multi-scale entanglement renormalization ansatz (MERA), we propose a principle of directed influence which asserts that the tensors in the MERA’s that represent the ground states can be chosen to be identical everywhere except within a specific, localized region of the tensor network.  The validity of this principle is just

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Quantum Spin Liquids,Density Matrix Renormalization Group, and Entanglement

Thursday May 09, 2013
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I will review recent work in our group using Density Matrix Renormalization Group (DMRG) to search for and study quantum spin liquid and topologically ordered states in two dimensional model Hamiltonians. This proves an efficient way to study these phases in semi-realistic situations.  I will try to draw lessons from several studies and theoretical considerations.

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Searching for Spin Liquids

Thursday May 09, 2013
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Holographic insights into quantum critical transport: from branes to Bose-Hubbard

Wednesday May 08, 2013

We discuss the general features of charge transport of quantum critical points described by CFTs in 2+1D. Our main tool is the AdS/CFT correspondence, but we will make connections to standard field theory results and to recent quantum Monte Carlo data. We emphasize the importance of poles and zeros of the response functions. In the holographic setting, these are the discrete quasinormal modes of a black hole/brane; they map to the excitations of the CFT.

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Wednesday May 08, 2013
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In this talk, I will discuss about the notion of quantum renormalization group, and explain how (D+1)-dimensional gravitational theories naturally emerge as dual descriptions for D-dimensional quantum field theories. It will be argued that the dynamical gravitational field in the bulk encodes the entanglement between low energy modes and high energy modes of the corresponding quantum field theory.

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Propagation of entanglement in strongly coupled systems from gravity

Wednesday May 08, 2013
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Thermodynamical Property of Entanglement Entropy for Excited States

Wednesday May 08, 2013
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We will point out that there is a universal thermodynamical property of entanglement entropy for excited states.  We will derive this by using the AdS/CFT correspondence in any dimension. We will also directly confirm this property from direct field theoretic calculations in two dimensions. We will define a new quantity called entanglement density by taking derivatives of entanglement entropy with respect to the shape of subsystem.

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Impossible symmetry enriched topological phases in 2D and their realization on 3D surface

Tuesday May 07, 2013
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In quantum systems with symmetry, the same topological phase can be enriched by symmetry in different ways, resulting in different symmetry transformations of the superselection sectors in the phase. However, not all symmetry transformations are allowed on the superselection sectors in topological phases in purely 2D systems.

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3D topological lattice models with topologically ordered surface states

Tuesday May 07, 2013
Speaker(s):

I will discuss a family of solvable 3D lattice models that have a trivial" bulk, in which all excitations are confined, but exhibit topologically ordered surface states.  I will discuss perturbations to these models that can drive a phase transition in which some of these excitations become deconfined, driving the system into a phase with bulk topological order.

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