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Eigenstate Thermalization Hypothesis in Conformal …

We show that this model satisfies the eigenstate thermalization hypothesis by solving the system in exact diagonalization.

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of view of the eigenstate thermalization hypothesis.

To this end, we perform an ab initio numericalanalysis of a system of hard-core bosons on a lattice and show [MarcosRigol, Vanja Dunjko & Maxim Olshanii, Nature 452, 854 (2008)] thatthe above controversy can be resolved via the Eigenstate ThermalizationHypothesis suggested independently by Deutsch [J.

Eigenstate thermalization hypothesis in quantum ..

According to this hypothesis, in quantum systems thermalizationhappens in each individual eigenstate of the system separately, but itis hidden initially by coherences between them.

A seemingly paradox for Eigenstate Thermalization Hypothesis ..

We investigate the eigenstate thermalization hypothesis (ETH) inintegrable models, focusing on the spin-1/2 isotropic Heisenberg (X X X) chain.

N2 - Many phases of matter, including superconductors, fractional quantum Hall fluids, and spin liquids, are described by gauge theories with constrained Hilbert spaces. However, thermalization and the applicability of quantum statistical mechanics has primarily been studied in unconstrained Hilbert spaces. In this paper, we investigate whether constrained Hilbert spaces permit local thermalization. Specifically, we explore whether the eigenstate thermalization hypothesis (ETH) holds in a pinned Fibonacci anyon chain, which serves as a representative case study. We first establish that the constrained Hilbert space admits a notion of locality by showing that the influence of a measurement decays exponentially in space. This suggests that the constraints are no impediment to thermalization. We then provide numerical evidence that ETH holds for the diagonal and off-diagonal matrix elements of various local observables in a generic disorder-free nonintegrable model. We also find that certain nonlocal observables obey ETH.

AB - Many phases of matter, including superconductors, fractional quantum Hall fluids, and spin liquids, are described by gauge theories with constrained Hilbert spaces. However, thermalization and the applicability of quantum statistical mechanics has primarily been studied in unconstrained Hilbert spaces. In this paper, we investigate whether constrained Hilbert spaces permit local thermalization. Specifically, we explore whether the eigenstate thermalization hypothesis (ETH) holds in a pinned Fibonacci anyon chain, which serves as a representative case study. We first establish that the constrained Hilbert space admits a notion of locality by showing that the influence of a measurement decays exponentially in space. This suggests that the constraints are no impediment to thermalization. We then provide numerical evidence that ETH holds for the diagonal and off-diagonal matrix elements of various local observables in a generic disorder-free nonintegrable model. We also find that certain nonlocal observables obey ETH.

Stron eigenstate thermalization hypothesis - Open …

Eigenstate thermalization hypothesis and integrability …

Progress in physics and quantum information science motivates much recent study of the behavior of extensively-entangled many-body quantum systems fully isolated from their environment, and thus undergoing unitary time evolution. What does it mean for such a system to go to thermal equilibrium? I will explain the Eigenstate Thermalization Hypothesis (ETH), which posits that each individual exact eigenstate of the system's Hamiltonian is at thermal equilibrium, and which appears to be true for many (but not all) quantum many-body systems. Prominent among the systems that do not obey this hypothesis are quantum systems that are many-body Anderson localized and thus do not constitute a reservoir that can thermalize itself. When the ETH is true, one can do standard statistical mechanics using the `single-eigenstate ensembles', which are the limit of the microcanonical ensemble where the `energy window' contains only a single many-body eigenstate. These eigenstate e nsembles are more powerful than the traditional statistical mechanical ensembles, in that they can also "see" the novel quantum phase transition in to the many-body localized phase, as well as a rich new world of many-body localized phases with symmetry-breaking and/or topological order.

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. 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. 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, 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 that is widely expected but very 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 explicitly demonstrates how statistical physics emerges from entanglement in a single eigenstate.

Eigenstate thermalization hypothesis in quantum dimer …
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  • Eigenstate thermalization hypothesis and quantum …

    The eigenstate thermalization hypothesis in constrained Hilbert spaces: A case study in non-Abelian anyon chains

  • eigenstate thermalization hypothesis.

    Pushing the Limits of the Eigenstate Thermalization Hypothesis towards Mesoscopic Quantum Systems

  • I will explain the Eigenstate Thermalization Hypothesis ..

    I will then introduce the so-called Eigenstate Thermalization Hypothesis (ETH) ansatz first proposed by J

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PERSPECTIVE OF EIGENSTATE THERMALIZATION ..

Many phases of matter, including superconductors, fractional quantum Hall fluids, and spin liquids, are described by gauge theories with constrained Hilbert spaces. However, thermalization and the applicability of quantum statistical mechanics has primarily been studied in unconstrained Hilbert spaces. In this paper, we investigate whether constrained Hilbert spaces permit local thermalization. Specifically, we explore whether the eigenstate thermalization hypothesis (ETH) holds in a pinned Fibonacci anyon chain, which serves as a representative case study. We first establish that the constrained Hilbert space admits a notion of locality by showing that the influence of a measurement decays exponentially in space. This suggests that the constraints are no impediment to thermalization. We then provide numerical evidence that ETH holds for the diagonal and off-diagonal matrix elements of various local observables in a generic disorder-free nonintegrable model. We also find that certain nonlocal observables obey ETH.

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