Canonical Thermal Pure Quantum State

Sugiura, Sho; Shimizu, Akira

doi:10.1103/physrevlett.111.010401

Cited by 228 publications

(365 citation statements)

References 15 publications

(30 reference statements)

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“…See also [2,6]. 7 In [14,15], the term 'thermal pure quantum states' has been coined for pure states representing thermal equilibrium. 8 When the (rounded) observables … M M , ,ˆk 1 commute with each other and also with the projection onto , then we choose  eq as the subspace spanned by simultaneous eigenstates of…”

Section: Setting Background and Main Resultsmentioning

confidence: 99%

“…It has been demonstrated in some general or concrete settings that a pure initial state evolving under quantum dynamics indeed equilibrates or thermalizes 4 in a certain mathematical sense [3][4][5][6][7][8][9][10]. See also [11][12][13][14][15] for closely related idea that a typical pure state of a macroscopic quantum system can fully describe thermal equilibrium.…”

Section: Introductionmentioning

confidence: 99%

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Extremely quick thermalization in a macroscopic quantum system for a typical nonequilibrium subspace

2015

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Extremely quick thermalization in a macroscopic quantum system for a typical nonequilibrium subspace AbstractThe fact that macroscopic systems approach thermal equilibrium may seem puzzling, for example, because it may seem to conflict with the time-reversibility of the microscopic dynamics. We here prove that in a macroscopic quantum system for a typical choice of 'nonequilibrium subspace', any initial state indeed thermalizes, and in fact does so very quickly, on the order of the Boltzmann time τ = h k T :. Therefore what needs to be explained is, not that macroscopic systems approach thermal equilibrium, but that they do so slowly.

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Section: Setting Background and Main Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Extremely quick thermalization in a macroscopic quantum system for a typical nonequilibrium subspace

2015

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“…1.7 N = 16 sites, and is estimated by employing thermal pure quantum states 20,21 for the 24-and 32-site clusters with the periodic boundary condition. The finite size clusters used in the following are illustrated in Fig.1…”

Section: B Specific Heatmentioning

confidence: 99%

Clues and criteria for designing a Kitaev spin liquid revealed by thermal and spin excitations of the honeycomb iridateNa2IrO3

et al. 2016

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Contrary to the original expectation, Na2IrO3 is not a Kitaev's quantum spin liquid (QSL) but shows a zig-zag-type antiferromagnetic order in experiments. Here we propose experimental clues and criteria to measure how a material in hand is close to the Kitaev's QSL state. For this purpose, we systematically study thermal and spin excitations of a generalized Kitaev-Heisenberg model studied by Chaloupka et al. in Phys. Rev. Lett. 110, 097204 (2013) and an effective ab initio Hamiltonian for Na2IrO3 proposed by Yamaji et al. in Phys. Rev. Lett. 113, 107201 (2014), by employing a numerical diagonalization method. We reveal that closeness to the Kitaev's QSL is characterized by the following properties, besides trivial criteria such as reduction of magnetic ordered moments and Néel temperatures: (1) Two peaks in the temperature dependence of specific heat at T ℓ and T h caused by the fractionalization of spin to two types of Majorana fermions. (2) In between the double peak, prominent plateau or shoulder pinned at R 2 ln 2 in the temperature dependence of entropy, where R is the gas constant. (3) Failure of the linear spin wave approximation at the low-lying excitations of dynamical structure factors. (4) Small ratio T ℓ /T h close to or less than 0.03. According to the proposed criteria, Na2IrO3 is categorized to a compound close to the Kitaev's QSL, and is proven to be a promising candidate for the realization of the QSL if the relevant material parameters can further be tuned by making thin film of Na2IrO3 on various substrates or applying axial pressure perpendicular to the honeycomb networks of iridium ions. Applications of these characterization to (Na1−xLix)2IrO3 and other related materials are also discussed.

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“…While this question has a long and fertile history, it has attracted continuously increasing attention in the last decade [1,2]. This upsurge of interest is also related to the advent of novel materials and cold atomic gases [3,4], the discovery of new states of matter such as many-body localized phases [5][6][7], the invention of powerful numerical techniques such as density-matrix renormalization group [8,9], as well as the emergence of fresh key concepts, with typicality of pure states [10][11][12][13][14][15][16][17][18][19][20][21] and eigenstate thermalization hypothesis [22][23][24] as prime examples. Although clarifying the mere existence of equilibration and thermalization in isolated systems has seen substantial progress [25,26], rigorously deriving the macroscopic phenomena of (exponential) relaxation and (diffusive) transport from truly microscopic principles is still a major challenge [27,28].…”

Section: Introductionmentioning

confidence: 99%

Real-time dynamics of typical and untypical states in nonintegrable systems

Richter¹,

Jin²,

Raedt³

et al. 2018

Phys. Rev. B

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Understanding (i) the emergence of diffusion from truly microscopic principles continues to be a major challenge in experimental and theoretical physics. At the same time, isolated quantum many-body systems have experienced an upsurge of interest in recent years. Since in such systems the realization of a proper initial state is the only possibility to induce a nonequilibrium process, understanding (ii) the largely unexplored role of the specific realization is vitally important. Our work reports a substantial step forward and tackles the two issues (i) and (ii) in the context of typicality, entanglement as well as integrability and nonintegrability. Specifically, we consider the spin-1/2 XXZ chain, where integrability can be broken due to an additional next-nearest neighbor interaction, and study the real-time and real-space dynamics of nonequilibrium magnetization profiles for a class of pure states. Summarizing our main results, we show that signatures of diffusion for strong interactions are equally pronounced for the integrable and nonintegrable case. In both cases, we further find a clear difference between the dynamics of states with and without internal randomness. We provide an explanation of this difference by a detailed analysis of the local density of states.

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Canonical Thermal Pure Quantum State

Cited by 228 publications

References 15 publications

Extremely quick thermalization in a macroscopic quantum system for a typical nonequilibrium subspace

Extremely quick thermalization in a macroscopic quantum system for a typical nonequilibrium subspace

Clues and criteria for designing a Kitaev spin liquid revealed by thermal and spin excitations of the honeycomb iridateNa2IrO3

Real-time dynamics of typical and untypical states in nonintegrable systems

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