Explicit Hamiltonians inducing volume law for entanglement entropy in fermionic lattices

Gori, Giacomo; Paganelli, Simone; Sharma, Auditya; Sodano, P.; Trombettoni, Andrea

doi:10.1103/physrevb.91.245138

Cited by 48 publications

(47 citation statements)

References 94 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One famous example is noncommutative geometry and noncommutative quantum field theory [6]. Other examples are systems with long range couplings preserving translational symmetry [7].…”

Section: Introduction and Description Of Resultsmentioning

confidence: 99%

Black holes as random particles: entanglement dynamics in infinite range and matrix models

Magán

2016

J. High Energ. Phys.

View full text Add to dashboard Cite

We first propose and study a quantum toy model of black hole dynamics. The model is unitary, displays quantum thermalization, and the Hamiltonian couples every oscillator with every other, a feature intended to emulate the color sector physics of large-N matrix models. Considering out of equilibrium initial states, we analytically compute the time evolution of every correlator of the theory and of the entanglement entropies, allowing a proper discussion of global thermalization/scrambling of information through the entire system. Microscopic non-locality causes factorization of reduced density matrices, and entanglement just depends on the time evolution of occupation densities. In the second part of the article, we show how the gained intuition extends to large-N matrix models, where we provide a gauge invariant entanglement entropy for 'generalized free fields', again depending solely on the quasinormal frequencies. The results challenge the fast scrambling conjecture and point to a natural scenario for the emergence of the so-called brick wall or stretched horizon. Finally, peculiarities of these models in regards to the thermodynamic limit and the information paradox are highlighted.

show abstract

“…One famous example is noncommutative geometry and noncommutative quantum field theory [6]. Other examples are systems with long range couplings preserving translational symmetry [7].…”

Section: Introduction and Description Of Resultsmentioning

confidence: 99%

Black holes as random particles: entanglement dynamics in infinite range and matrix models

Magán

2016

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…area law (24). More recently, Gori et al (25) argued that in translationally invariant models a fractal structure of the Fermi surface is necessary for maximum violation of entanglement entropy, and using nonlocal field theories volume-law scaling was argued using simple constructions (26). Independently from ref.…”

Section: Significancementioning

confidence: 99%

Supercritical entanglement in local systems: Counterexample to the area law for quantum matter

Movassagh

Shor

2016

Proc. Natl. Acad. Sci. U.S.A.

108

178

View full text Add to dashboard Cite

Quantum entanglement is the most surprising feature of quantum mechanics. Entanglement is simultaneously responsible for the difficulty of simulating quantum matter on a classical computer and the exponential speedups afforded by quantum computers. Ground states of quantum many-body systems typically satisfy an "area law": The amount of entanglement between a subsystem and the rest of the system is proportional to the area of the boundary. A system that obeys an area law has less entanglement and can be simulated more efficiently than a generic quantum state whose entanglement could be proportional to the total system's size. Moreover, an area law provides useful information about the low-energy physics of the system. It is widely believed that for physically reasonable quantum systems, the area law cannot be violated by more than a logarithmic factor in the system's size. We introduce a class of exactly solvable one-dimensional physical models which we can prove have exponentially more entanglement than suggested by the area law, and violate the area law by a square-root factor. This work suggests that simple quantum matter is richer and can provide much more quantum resources (i.e., entanglement) than expected. In addition to using recent advances in quantum information and condensed matter theory, we have drawn upon various branches of mathematics such as combinatorics of random walks, Brownian excursions, and fractional matching theory. We hope that the techniques developed herein may be useful for other problems in physics as well.quantum matter | local Hamiltonians entanglement entropy | area law | spin chains | Hamiltonian gap S tudy of quantum many-body systems (QMBSs) is the study of quantum properties of matter and quantum resources (e.g., entanglement) provided by matter for building revolutionary new technologies such as a quantum computer. One of the properties of the QMBS is the amount of entanglement among parts of the system (1, 2). Entanglement can be used as a resource for quantum technologies and information processing (2-5); however, at a fundamental level it provides information about the quantum state of matter, such as near-criticality (6, 7). Moreover, systems with high entanglement are usually hard to simulate on a classical computer (8). How much entanglement do natural QMBSs possess? What are the fundamental limits on simulation of physical systems?The area law says that entanglement entropy between two subsystems of a system is proportional to the area of the boundary between them. A generic state does not obey an area law (9); therefore, obeying an area law implies that a QMBS contains much less quantum correlation than generically expected. One can imagine that any given system has inherent constraints such as underlying symmetries and locality of interaction that restrict the states to reside on special submanifolds rendering their simulation efficient (10).Since the discovery that the Affleck-Kennedy-Lieb-Tasaki (AKLT) model (11) is exactly solvable, and that the density matrix re...

show abstract

“…A possible way to create a nontrivial Fermi surface is to introduce a gauge potential [80]. Let us consider a model with long-range hopping with periodic boundary conditions:…”

Section: Violation Of the Area-law In Long-range Systemsmentioning

confidence: 99%

Abelian Gauge Potentials on Cubic Lattices

Burrello

Lepori

Paganelli

et al. 2017

Advances in Quantum Mechanics

View full text Add to dashboard Cite

The study of the dynamics of a quantum particle in a magnetic field is a fascinating subject of perduring interest both in physics and mathematics literature. The quantization of energy levels giving rise to the Landau levels is at the basis of our understanding of integer and fractional quantum Hall effects [1, 2, 3, 4, 5] and its higher-dimensional counterparts and generalizations, including topological insulators [6,7,8]. The use of vector potentials in quantum mechanics is associated in itself to very interesting consequences, such as the purely quantum mechanical interference in the Aharonov-Bohm effect [9]. On the other side, the mathematical formalism for a particle in a magnetic field has been developed and refined along the time, based on the rigorous definition of Schrödinger operators with magnetic fields [10]. An important role is played by the construction of families of observables in the presence of gauge fields relying on the progresses in gauge covariant

show abstract

Explicit Hamiltonians inducing volume law for entanglement entropy in fermionic lattices

Cited by 48 publications

References 94 publications

Black holes as random particles: entanglement dynamics in infinite range and matrix models

Black holes as random particles: entanglement dynamics in infinite range and matrix models

Supercritical entanglement in local systems: Counterexample to the area law for quantum matter

Abelian Gauge Potentials on Cubic Lattices

Contact Info

Product

Resources

About