Quantum Matter: Emergence & Entanglement 3
Recent experiments in graphene heterostructures have observed Chern insulators - integer and fractional Quantum Hall states made possible by a periodic substrate potential. Here we study theoretically that the competition between different Chern insulators, which can be tuned by the amplitude of the periodic potential, leads to a new family of quantum critical points described by QED3-Chern-Simons theory.
The conventional Euclidean time Monte Carlo approach to Lattice Field Theories faces a major obstacle in the sign problem in certain parameter regimes, such as the presence of a nonzero chemical potential or a topological theta-term. Tensor Network States, a family of ansatzes for the efficient description of quantum many-body states, offer a promising alternative for addressing Lattice Field Theories in the Hamiltonian formulation.
We give rigorous analytical results on the temporal behavior of two-point correlation functions (also known as dynamical response functions or Green’s functions) in quantum many body systems undergoing unitary dynamics. Using recent results from large deviation theory, we show that in a large class of models the correlation functions factorize at late times -> , thus proving that dissipation emerges out of the unitary dynamics of the system.
Key to characterizing universality in critical systems is the identification of the RG fixed point, which is very often a conformal field theory (CFT). We show how to use lattice operators that mimic the Virasoro generators of conformal symmetry to systematically extract, from a generic critical quantum spin chain, a complete set of the conformal data (central charge, scaling dimensions of primary fields, OPE coefficients) specifying a 2D CFT.
We discuss recent progress in theory and experiment on emergent topological phases in Kitaev materials. Here the competition between different anisotropic spin-exchange interactions may lead to a number of exotic phases of matter. We investigate possible emergence of quantum spin liquid, topological magnons, and topological superconductivity in two and three dimensional systems. We make connections to existing and future experiments.
It is an open question how well tensor network states in the form of an infinite projected entangled-pair states (iPEPS) tensor network can approximate gapless quantum states of matter. In this talk we address this issue for two different physical scenarios: (i) a conformally invariant (2+1)d quantum critical point in the incarnation of the transverse-field Ising model on the square lattice and (ii) spontaneously broken continuous symmetries with gapless Goldstone modes exemplified by the S=1/2 antiferromagnetic Heisenberg and XY models on the square lattice.
In the first half, I will demonstrate an efficient and general approach for realizing non-trivial quantum states, such as quantum critical and topologically ordered states, in quantum simulators. In the second half, I will present a related variational ansatz for many-body quantum systems that is remarkably efficient. In particular, representing the critical point of the one-dimensional transverse field Ising model only requires a number of variational parameters scaling logarithmically with system size.
We introduce an isometric restriction of the tensor-network ansatz that allows for highly efficient contraction of the network. We consider two concrete applications using this ansatz. First, we show that a matrix-product state representation of a 2D quantum state can be iteratively transformed into an isometric 2D tensor network. Second, we introduce a 2D version of the time-evolving block decimation algorithm (TEBD2) for approximating the ground state of a Hamiltonian as an isometric tensor network, which we demonstrate for the 2D transverse field Ising model.
In the context of quantum spin liquids, it is long known that the condensation of fractionalized excitations will inevitably break certain physical symmetries sometimes. For example, condensing spinons will usually break spin rotation and time reversal symmetries. We generalize these phenomena to generic continuous quantum phase transitions between symmetry enriched topological orders driven by anyon condensation. We provide a generic rule to determine whether a symmetry is enforced to break across an anyon condensation transition.