Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session M52: Invited Session: Entanglement in Condensed Matter Systems |
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Sponsoring Units: DCMP Chair: Joel Moore, University of California, Berkeley Room: Grand Ballroom C2 |
Wednesday, March 4, 2015 11:15AM - 11:51AM |
M52.00001: Entanglement Hamiltonians in Fermion Systems and the Riemann-Hilbert problem Invited Speaker: Israel Klich In this talk, I will discuss work on entanglement in fermion systems. I will describe recent results on effective entanglement hamiltonians in conformal quantum field theories, and how the free fermion entanglement Hamiltonian in 1d can be obtained by solving a Riemann-Hilbert problem. I will also show how finite size corrections to the Hamiltonian may be obtained by perturbing around the Riemann-Hilbert solutions, as well as explore subtle difference between the Neveu-Schwartz and Ramond sectors of free fermion fields. [Preview Abstract] |
Wednesday, March 4, 2015 11:51AM - 12:27PM |
M52.00002: Entanglement Scaling Laws and Eigenstate Thermalization in Many-Particle Systems Invited Speaker: Kun Yang While entanglement entropy of ground states usually follows the area law, violations do exist, and it is important to understand their origin. In 1D they are found to be associated with quantum criticality. Until recently the only established examples of such violation in higher dimensions are free fermion ground states with Fermi surfaces, where it is found that the area law is enhanced by a logarithmic factor. In Ref. [1], we use multi-dimensional bosonization to provide a simple derivation of this result, and show that the logarithimic factor has a 1D origin. More importantly the bosonization technique allows us to take into account the Fermi liquid interactions, and obtain the leading scaling behavior of the entanglement entropy of Fermi liquids. The central result of our work is that Fermi liquid interactions do not alter the leading scaling behavior of the entanglement entropy, and the logarithmic enhancement of area law is a robust property of the Fermi liquid phase. In sharp contrast to the fermioic systems with Fermi surfaces, quantum critical (or gapless) bosonic systems do not violate the area law above 1D (except for the case discussed below). The fundamental difference lies in the fact that gapless excitations live near a single point (usually origin of momentum space) in such bosonic systems, while they live around an (extended) Fermi surface in Fermi liquids. In Ref. [2], we studied entanglement properties of some specific examples of the so called Bose metal states, in which bosons neither condense (and become a superfluid) nor localize (and insulate) at T=0. The system supports gapless excitations around ``Bose surfaces," instead of isolated points in momentum space. We showed that similar to free Fermi gas and Fermi liquids, these states violate the entanglement area law in a logarithmic fashion. Compared to ground states, much less is known concretely about entanglement in (highly) excited states. Going back to free fermion systems, in Ref. [3] we show that there exists a duality relation between ground and excited states, and the area law obeyed by ground state turns into a volume law for excited states, something widely expected but hard to prove. Most importantly, we find in appropriate limits the reduced density matrix of a subsystem takes the form of thermal density matrix, providing an explicit example of the eigenstate thermalization hypothesis. Our work [3] explicitly demonstrates how statistical physics emerges from entanglement in a single eigenstate.\\[4pt] [1] Entanglement Entropy of Fermi Liquids via Multi-dimensional Bosonization, Wenxin Ding, Alexander Seidel, Kun Yang, Phys. Rev. X 2, 011012 (2012).\\[0pt] [2] Violation of Entanglement-Area Law in Bosonic Systems with Bose Surfaces: Possible Application to Bose Metals, Hsin-Hua Lai, Kun Yang, N. E. Bonesteel, Phys. Rev. Lett. 111, 210402 (2013).\\[0pt] [3] Entanglement entropy scaling laws and eigenstate thermalization in free fermion systems, Hsin-Hua Lai, Kun Yang, arXiv:1409.1224. [Preview Abstract] |
Wednesday, March 4, 2015 12:27PM - 1:03PM |
M52.00003: Entanglement and Stability of Quantum Matter: from Spin-liquids to Many Body Localization Invited Speaker: Tarun Grover Quantum entanglement often serves as a fruitful order parameter to characterize quantum phases and phase transitions. However, recent developments have lead to a completely new role for quantum entanglement: the nature of quantum entanglement also places strong constraints on the structure of \textit{phase diagrams} itself. Specifically, the universal part of entanglement provides a natural ordering for critical systems whereby a critical, scale-invariant phase can be unstable only if the instability reduces entanglement. In this talk, I will elucidate implications of the aforementioned general relation between entanglement and critical phases for a wide variety of challenging problems in condensed matter physics. I will first discuss general arguments on why a large class of gapless quantum spin-liquids, which possess exotic properties such as emergent fermions and photons, must be stable. In a similar vein, I will show that certain quantum transitions must lie beyond a simple Landau order parameter description. Finally, I will discuss a generalization of such arguments to disordered quantum systems in the context of many-body localization transition. Specifically, I will show that at a continuous many-body localization transition, the system is necessarily ergodic. [Preview Abstract] |
Wednesday, March 4, 2015 1:03PM - 1:39PM |
M52.00004: Einstein's Equations From Entanglement Invited Speaker: Brian Swingle I will outline a path by which a semi-classical geometry obeying Einstein's equations emerges holographically from entanglement in certain quantum many-body systems. Although some challenges remain, I will argue that the core concepts are in place. I will discuss in particular two crucial results, one establishing the existence of tensor networks for a wide class of quantum many-body systems, and one showing how the equivalence principle is encoded in the universality of entanglement. The first result establishing the existence of tensor networks has independent interest for the classical simulation of quantum many-body physics. [Preview Abstract] |
Wednesday, March 4, 2015 1:39PM - 2:15PM |
M52.00005: Quantum Entanglement and the Topological Order of Fractional Hall States Invited Speaker: Edward Rezayi Fractional quantum Hall states or, more generally, topological phases of matter defy Landau classification based on order parameter and broken symmetry. Instead they have been characterized by their topological order. Quantum information concepts, such as quantum entanglement, appear to provide the most efficient method of detecting topological order solely from the knowledge of the ground state wave function. This talk will focus on real-space bi-partitioning of quantum Hall states and will present both exact diagonalization and quantum Monte Carlo studies of topological entanglement entropy in various geometries. Results on the torus for non-contractible cuts are quite rich and, through the use of minimum entropy states, yield the modular S-matrix and hence uniquely determine the topological order, as shown in recent literature. Concrete examples of minimum entropy states from known quantum Hall wave functions and their corresponding quantum numbers, used in exact diagonalizations, will be given. [Preview Abstract] |
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