Thermalization and Canonical Typicality in Translation-Invariant Quantum Lattice Systems

Müller, Markus P.; Adlam, Emily; Masanes, Lluís; Wiebe, Nathan

doi:10.1007/s00220-015-2473-y

Cited by 112 publications

(173 citation statements)

References 33 publications

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“…In order to have thermalization of all initial states that can realistically be prepared, it seems that one does not need the ETH to be true for absolutely all eigenstates; a weaker almost all should suffice. And if we look at the numerical results, they do strongly support the proposal that there are systems where at least almost all eigenstates obey the ETH [13,[47][48][49][50][51][52][53][54][55][56][57][58]. But the simpler and it seems more plausible scenario is that if the ETH is true for a given system at a given temperature, then it is true there for all eigenstates.…”

Section: B the Eigenstate Thermalization Hypothesismentioning

confidence: 63%

Many-Body Localization and Thermalization in Quantum Statistical Mechanics

Nandkishore

Huse²

2015

Annu. Rev. Condens. Matter Phys.

2,417

2,415

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We review some recent developments in the statistical mechanics of isolated quantum systems.We provide a brief introduction to quantum thermalization, paying particular attention to the 'Eigenstate Thermalization Hypothesis' (ETH), and the resulting 'single-eigenstate statistical mechanics'. We then focus on a class of systems which fail to quantum thermalize and whose eigenstates violate the ETH: These are the many-body Anderson localized systems; their long-time properties are not captured by the conventional ensembles of quantum statistical mechanics. These systems can locally remember forever information about their local initial conditions, and are thus of interest for possibilities of storing quantum information. We discuss key features of many-body localization (MBL), and review a phenomenology of the MBL phase. Single-eigenstate statistical mechanics within the MBL phase reveals dynamically-stable ordered phases, and phase transitions among them, that are invisible to equilibrium statistical mechanics and can occur at high energy and low spatial dimensionality where equilibrium ordering is forbidden.

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Section: B the Eigenstate Thermalization Hypothesismentioning

confidence: 63%

Many-Body Localization and Thermalization in Quantum Statistical Mechanics

Nandkishore

Huse²

2015

Annu. Rev. Condens. Matter Phys.

2,417

2,415

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“…Random unitary transformations are often considered in the form of random quantum circuits, with wide-ranging applications in, for example, estimating noise [1], private channels [2], modelling thermalisation [3], photonics [4], and even black hole physics [5]. Uniform randomness -sampling from the 'flat' measure on a continuous set -is however very resource intensive.…”

mentioning

confidence: 99%

Derandomizing Quantum Circuits with Measurement-Based Unitary Designs

Turner

Markham

2016

Phys. Rev. Lett.

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Entangled multipartite states are resources for universal quantum computation, but they can also give rise to ensembles of unitary transformations, a topic usually studied in the context of random quantum circuits. Using several graph state techniques, we show that these resources can 'derandomize' circuit results by sampling the same kinds of ensembles quantum mechanically, analogously to a quantum random number generator. Furthermore, we find simple examples that give rise to new ensembles whose statistical moments exactly match those of the uniformly random distribution over all unitaries up to order t, while foregoing adaptive feed-forward entirely. Such ensembles -known as t-designs -often cannot be distinguished from the 'truly' random ensemble, and so they find use in many applications that require this implied notion of pseudorandomness.Introduction -Randomness is an important resource in both classical and quantum information theory, underpinning cryptography, characterisation, and simulation. Random unitary transformations are often considered in the form of random quantum circuits, with wide-ranging applications in, for example, estimating noise[1], private channels[2], modelling thermalisation[3], photonics [4], and even black hole physics [5]. Uniform randomness -sampling from the 'flat' measure on a continuous set -is however very resource intensive. A natural definition of a less costly pseudorandom ensemble is one whose statistical moments are equal to those of the uniform ensemble up to some finite order t -this is the defining property of a t-design. Analogous to combinatorial designs that arise in many areas [6], in the quantum community the concept was first applied to states [7], and later to processes [8], the latter being the topic of much recent work (e.g. [9]) and are our concern here.

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“…Then, the state (6) is the typical one for which the canonical typicality takes place [34,35]. Namely, for small subset of m N + 1 TLS the state of these m TLS averaged over the rest of the chain, is very close to the to the Gibbs state ρ [36]. Thus, for the state of the chain weakly deviating from the symmetric one (6), one can meaningfully introduce the temperature as T = ω/kβ, and derive the continuous heat-transfer equation.…”

Section: Non-classicalitymentioning

confidence: 96%

Diffusive lossless energy and coherence transfer by noisy coupling

Mogilevtsev

Slepyan

2016

Phys. Rev. A

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Here we show that noisy coupling can lead to diffusive lossless energy transfer between individual quantum systems retaining a quantum character leading to entangled stationary states. Coherence might flow diffusively while being summarily preserved even when energy exchange is absent. Diffusive dynamics persists even in the case when additional noise suppresses all the unitary excitation exchange: arbitrarily strong local dephasing, while destroying quantum correlations, is not affecting energy transfer. IntroductionDiffusive transfer of energy (and, ultimately, derivation of Fourier heat-transfer law from microscopic dynamics) up to day remain subjects of theoretical interest and even controversy [1][2][3][4][5]. For microscopic dynamics dominated by quantum effects establishing of diffusive energy transfer is far from being obvious. Commonly considered microscopic models, such as chains of unitarily connected networks of bosonic and/or fermionic systems with attached thermal reservoirs and noise sources can demonstrate both ballistic and diffusive behavior in dependence on interaction strengths and other parameters of the whole system, generally requiring approximations (such as long time and large size limits) for emergence of classical-like heat dynamics. Here we suggest a noise-mediated microscopic mechanism for diffusive transfer. Energy can propagate without loss, but through losses. Recently it has become quite usual to see noises not only as something destroying quantum coherence and reducing quantum states to classicality, but also as a tool to create and enhance quantumness. Non-local loss can preserve entanglement and even generate entangled stated from initially uncorrelated ones [6][7][8][9][10]. Engineered loss can lead to dissipative protection and coherence preservation [11][12][13] and deterministic creation of non-classical states [14,[17][18][19][20] and serve as a tool for quantum computing [15,16]. Networks of dissipatively coupled systems can support topologically protected states [21]. Even a pure local dephasing is no longer considered completely harmful: it can enhance quantum state transfer and suppress localizing effects of static disorder [22][23][24]. However, too strong local dephasing generally suppresses unitary excitation exchange and energy transfer stemming from it.Here we show a microscopic mechanism of diffusive lossless energy transfer, which is impervious to local dephasing. It arises when coupling constants describing common single-excitation hopping are fluctuating randomly, like it is, for example, with spin-spin dipolar coupling in random environments. Dynamics produced by fluctuating coupling might preserve certain quantum correlations, and even entanglement during evolution toward the stationary state. Populations are not coupled by the dynamics with the off-diagonal terms. So, for example,

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Thermalization and Canonical Typicality in Translation-Invariant Quantum Lattice Systems

Cited by 112 publications

References 33 publications

Many-Body Localization and Thermalization in Quantum Statistical Mechanics

Many-Body Localization and Thermalization in Quantum Statistical Mechanics

Derandomizing Quantum Circuits with Measurement-Based Unitary Designs

Diffusive lossless energy and coherence transfer by noisy coupling

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