Scaling theory of entanglement entropy in confinements near quantum critical points

Cao, Xuanmin; Hu, Qijun; Zhong, Fan

doi:10.1103/physrevb.98.245124

Cited by 13 publications

(20 citation statements)

References 71 publications

(122 reference statements)

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“…For smaller Y values, as mentioned above, the system enters the finite-entanglement scaling regime and the surface bends down, as the surface of D = 100 exhibits. However, we note that both the shorttime regime and the finite-entanglement regime can be described by the same scaling form even though their leading behavior is different [83,100]. One reason that the overlap region is limited stem from the fact that the scaling theory is built on Eq.…”

Section: A Short-imaginary-time Critical Dynamics and The Kt Pointmentioning

confidence: 86%

“…( 10) can also be derived. On the other hand, if b = D κ , one finds 16) with yet another scaling function f D for finiteentanglement scaling because of the finite entanglement limited by the bond dimension [99,100]. Accordingly, ξ ∼ D κ asymptotically correctly.…”

Section: Short-time Critical Dynamicsmentioning

confidence: 96%

“…In TEBD, one has to take into account the bond dimension D [99,100], which is the number of states kept in matrix product states [101][102][103]. This is related to finite-entanglement scaling [99,100]. Moreover, we will study the short-time critical dynamics [88].…”

Section: Short-time Critical Dynamicsmentioning

confidence: 99%

“…( 1) fails. However, ξ obtained from a finite D may well be finite owing to the finite-entanglement scaling [100].…”

Section: Short-time Critical Dynamicsmentioning

confidence: 99%

“…Consequently, the standard error of the extrapolated 1/z is small, down to the fifth decimal place, even though the critical line, Eq. ( 50), has only three significant digits and usually the same number of digits is kept for the second-order Suzuki-Trotter expansion [100]. Now, we compute ξ for various J and D and repeat the above procedure for each J.…”

Section: A Short-imaginary-time Critical Dynamics and The Kt Pointmentioning

confidence: 99%

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Scaling Theories of Kosterlitz-Thouless Phase Transitions

Zuo,

Yin,

Cao

et al. 2021

Preprint

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We propose scaling theories for Kosterlitz-Thouless (KT) phase transitions on the basis of the hallmark exponential growth of their correlation length. Finite-size scaling, finite-entanglement scaling, short-time critical dynamics, and finite-time scaling, as well as some of their combinations are studied. Relaxation times of both a usual power-law and an unusual power-law with a logarithmic factor are considered. Finite-size and finite-entanglement scaling forms somehow similar to a frequently employed ansatz are presented. The Kibble-Zurek scaling of topological defect density for a linear driving across the KT transition point is investigated in detail. An implicit equation for a rate exponent in the theory is derived and the exponent varies with the distance from the critical point and the driving rate consistent with relevant experiments. To verify the theories, we utilize the KT phase transition of a one-dimensional Bose-Hubbard model. The infinite time-evolving-blockdecimation algorithm is employed to solve numerically the model for finite bond dimensions. Both a correlation length and an entanglement entropy in imaginary time and only the entanglement entropy in real-time driving are computed. Both the short-time critical dynamics in imaginary time and the finite-time scaling in real-time driving, both including the finite bond dimension, for the measured quantities are found to describe the numerical results quite well via surface collapses. The critical point is also estimated and confirmed to be 0.302(1) at the infinite bond dimension on the basis of the scaling form.

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Section: A Short-imaginary-time Critical Dynamics and The Kt Pointmentioning

confidence: 86%

Section: Short-time Critical Dynamicsmentioning

confidence: 96%

Section: Short-time Critical Dynamicsmentioning

confidence: 99%

“…( 1) fails. However, ξ obtained from a finite D may well be finite owing to the finite-entanglement scaling [100].…”

Section: Short-time Critical Dynamicsmentioning

confidence: 99%

Section: A Short-imaginary-time Critical Dynamics and The Kt Pointmentioning

confidence: 99%

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Scaling Theories of Kosterlitz-Thouless Phase Transitions

Zuo,

Yin,

Cao

et al. 2021

Preprint

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Self-Similarity Breaking: Anomalous Nonequilibrium Finite-Size Scaling and Finite-Time Scaling

Yuan¹,

Yin²,

Zhong³

2021

Chinese Phys. Lett.

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Symmetry breaking plays a pivotal role in modern physics. Although self-similarity is also a symmetry, and appears ubiquitously in nature, a fundamental question arises as to whether self-similarity breaking makes sense or not. Here, by identifying an important type of critical fluctuation, dubbed ‘phases fluctuations’, and comparing the numerical results for those with self-similarity and those lacking self-similarity with respect to phases fluctuations, we show that self-similarity can indeed be broken, with significant consequences, at least in nonequilibrium situations. We find that the breaking of self-similarity results in new critical exponents, giving rise to a violation of the well-known finite-size scaling, or the less well-known finite-time scaling, and different leading exponents in either the ordered or the disordered phases of the paradigmatic Ising model on two- or three-dimensional finite lattices, when subject to the simplest nonequilibrium driving of linear heating or cooling through its critical point. This is in stark contrast to identical exponents and different amplitudes in usual critical phenomena. Our results demonstrate how surprising driven nonequilibrium critical phenomena can be. The application of this theory to other classical and quantum phase transitions is also anticipated.

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Theory of Critical Phenomena with Memory

Zeng¹,

ping²,

Zhong³

2022

Chinese Phys. Lett.

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Memory is a ubiquitous characteristic of complex systems and critical phenomena are one of the most intriguing phenomena in nature. Here, we propose an Ising model with memory and develop a corresponding theory of critical phenomena with memory for complex systems and discovered a series of surprising novel results. We show that a naive theory of a usual Hamiltonian with a direct inclusion of a power-law decaying long-range temporal interaction violates radically a hyperscaling law for all spatial dimensions even at and below the upper critical dimension. This entails both indispensable consideration of the Hamiltonian for dynamics, rather than the usual practice of just focusing on the corresponding dynamic Lagrangian alone, and transformations that result in a correct theory in which space and time are inextricably interwoven, leading to an effective spatial dimension that repairs the hyperscaling law. The theory gives rise to a set of novel mean-field critical exponents, which are different from the usual Landau ones, as well as new universality classes. These exponents are verified by numerical simulations of the Ising model with memory in two and three spatial dimensions.

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Scaling theory of entanglement entropy in confinements near quantum critical points

Cited by 13 publications

References 71 publications

Scaling Theories of Kosterlitz-Thouless Phase Transitions

Scaling Theories of Kosterlitz-Thouless Phase Transitions

Self-Similarity Breaking: Anomalous Nonequilibrium Finite-Size Scaling and Finite-Time Scaling

Theory of Critical Phenomena with Memory

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