We study the effects of local projective measurements on the quantum quench dynamics. As a concrete example, one-dimensional Bose-Hubbard model is simulated by using matrix product state and time evolving block decimation. We map out a global phase diagram in terms of the measurement rate in spatial space and time domain, which demonstrates a volume-to-area law entanglement phase transition. When the measurement rates reach the critical values, we observe a logarithmic growth of entanglement entropy as the sub-system size or evolved time increases. This is akin to the character in the many-body localization, implying a general picture of the dynamical transitions separating quantum systems with different entanglement features. Moreover, we find that the probability distribution of the single-site entanglement entropy distinguishes the volume and area law phases just as the case of disorder-induced many-body localization. This suggests that the different type entanglement phase transitions may be understood as a nonlocalized-to-localized transition. We also investigate the scaling behavior of entanglement entropy and mutual information between two separated intervals, which is indicative of a single universality class and thus suggests a possible unified description of this transition.
The out-of-time-order correlators (OTOCs) is used to study the quantum phase transitions (QPTs) between the normal phase and the superradiant phase in the Rabi and few-body Dicke models with large frequency ratio of the atomic level splitting to the single-mode electromagnetic radiation field frequency. The focus is on the OTOC thermally averaged with infinite temperature, which is an experimentally feasible quantity. It is shown that the critical points can be identified by long-time averaging of the OTOC via observing its local minimum behavior. More importantly, the scaling laws of the OTOC for QPTs are revealed by studying the experimentally accessible conditions with finite frequency ratio and finite number of atoms in the studied models. The critical exponents extracted from the scaling laws of OTOC indicate that the QPTs in the Rabi and Dicke models belong to the same universality class.
This paper presents the first-principles calculation of the electron-phonon coupling and the temperature dependence of the intrinsic electrical resistivity of the zirconium-hydrogen system with various hydrogen concentrations. The nature of the anomalous decrease in the electrical resistivity of the Zr-H system with the increase of hydrogen concentration (at high concentrations of H/Zr>1.5) is studied. It was found that the hydrogen concentration, where the resistivity starts to decrease, is very close to the critical concentration of the δ-ε phase transition. It is shown that the tetragonal lattice distortion due to the δ-ε phase transition of the Zr-H system eliminates imaginary phonon frequencies and the strong electron-phonon coupling of the δ phase and, as a result, leads to the reduction of the electrical resistivity of the Zr-H system at a high hydrogen concentration.
We investigate the evolution of entanglement spectra under a global quantum quench from a short-range correlated state to the quantum critical point. Motivated by the conformal mapping, we find that the dynamical entanglement spectra demonstrates distinct finite-size scaling behaviors from the static case. As a prototypical example, we compute real-time dynamics of the entanglement spectra of a one-dimensional transverse-field Ising chain. Numerical simulation confirms that, the entanglement spectra scales with the subsystem size l as ∼ l −1 for the dynamical equilibrium state, much faster than ∝ log −1 l for the critical ground state. In particular, as a byproduct, the entanglement spectra at the long time limit faithfully gives universal tower structure of underlying Ising criticality, which shows the emergence of operator-state correspondence in the quantum dynamics.PACS numbers: 03.65. Ud, 11.25.Hf Conformal field theory (CFT) [1] has become a profitable tool as a diagnosis of critical phenomena in two dimensional statistical models. In the equilibrium case, the conformal invariance at the critical point sets rigid constrains on physical properties by a set of conformal data including the central charge, conformal dimensions and operator product expansion coefficients. In the past decades, great success has been achieved in condensed matter physics, especially for minimal models with a finite number of primary scaling operators (irreducible representations of the Virasoro algebra) [2][3][4][5][6].In general, due to gaplessness nature massive entanglement should play a vital role at or around the critical point. One remarkable achievement is [7-34], CFT provides a novel way to connect the quantum entanglement and critical phenomena. It is found that the conformal invariance in critical ground states results in a universal scaling of the entanglement entropy depending on the central charge c [8-10, 13, 16]. Interestingly, by extending this idea, the entropy can be applied to identify quantum critical points in higher dimensions [13,16,[35][36][37]. Besides the entropy, other entanglement-based measures also attract lots of attention. The eigenvalues of reduced density matrix, called entanglement spectrum (ES), is such an example, which contains much richer information than the entropy [38,39]. In addition to the evidences in topological gapped systems [40][41][42][43], the ES is also proposed to describe the quantum critical point [15,[44][45][46][47][48][49][50][51]. However, compared to the well-established boundary law for gapped states, much less is known about the critical behavior of the ES [52,53], which casts doubt on direct application of the ES in the critical systems.Beyond equilibrium, quantum dynamics attracts considerable attention recently, particular in approaching to steadiness and thermalization. Universal entanglement structures are expected to leave some marks in the dynamic process, e.g., central charge c controls the growth of entropy [11,17]. However, novel example [8] is still rare, a...
We calculate the thermal correction to the entanglement spectrum for separating a single interval of two dimensional conformal field theories. Our derivation is a direct extension of the thermal correction to the Rényi entropy. Within a low-temperature expansion by including only the first excited state in the thermal density matrix, we approach analytical results of the thermal correction to the entanglement spectrum at both of the small and large interval limit. We find the temperature correction reduces the large eigenvalues in the entanglement spectrum while increases the small eigenvalues in the entanglement spectrum, leading to an overall crossover changing pattern of the entanglement spectrum. Crucially, at low-temperature limit, the thermal corrections are dominated by the first excited state and depend on its scaling dimension ∆ and degeneracy g. This opens an avenue to extract universal information of underlying conformal data via the thermal entanglement spectrum. All of these analytical computation is supported from numerical simulations using 1+1 dimensional free fermion. Finally, we extend our calculation to resolve the thermal correction to the symmetry-resolved entanglement spectrum.
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