Nonequilibrium Dynamics of Deconfined Quantum Critical Point in Imaginary Time

Shu, Yu-Rong; Jian, Shao-Kai; Yin, Shuai

doi:10.1103/physrevlett.128.020601

Cited by 9 publications

(17 citation statements)

References 80 publications

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“…If z u = z, Eq. ( 4) recovers the usual single-length-scale relaxation scaling theory, in which, for instance, at the critical point, i.e., δ = 0, for a saturated initial state the order parameter scales as [91,93,99], while for a disordered initial state M 2 = L −d τ d/zu−2β/νzu f (τ L −zu ) in which the factor L −d stems from the random distribution of the initial state [93,99]. For both cases, in the long-time limit, the scaling form recovers the equilibrium case, namely, M 2 ∝ L −2β/ν [93,99].…”

Section: Brief Review Of the Dynamic Scaling In J-q3 Modelsupporting

confidence: 65%

“…A wide range of quantum Monte Carlo (QMC) methods, including the stochastic series expansion, projector QMC, and world line methods, have natural connections to simulations of the imaginary-time evolution of quantum spin systems [105]. In particular, the projector QMC has proven a powerful tool in pursuing the imaginary-time dynamics [96,97,99,[105][106][107][108][109][110]. In the projector QMC method, the imaginary-time evolution operator is Taylor-expanded and the normalization can then be written as the sum of the operator sequence acting on some suitable basis states, such as the S z basis, the valence bond basis etc [100,111].…”

Section: Model and Imaginary-time Relaxation Dynamicsmentioning

confidence: 99%

“…Therefore, different basis are applied for convenience. For the saturated VBS state, the valence bond basis is used [100,111], while for the AFM and disordered state, the S z basis is used [96,97,99,100,[105][106][107][108]110]. For more detailed introduction of the method, we refer to the literature [33,96,100,[105][106][107][108]112].…”

Section: Model and Imaginary-time Relaxation Dynamicsmentioning

confidence: 99%

“…In contrast, for the criticality with two length scales, there are two possibilities: (i) ξ ∝ τ 1/z and ξ ∝ τ ν /νz ; and (ii) ξ ∝ τ 1/z and ξ ∝ τ 1/zu with z u being z u ≡ zν /ν (The subscript u means the usual correlation length). It has been shown that scenario (ii) is selected by the DQCP in the J-Q 3 model [99].…”

Section: Brief Review Of the Dynamic Scaling In J-q3 Modelmentioning

confidence: 99%

“…Inspired by above intriguing issues, a nature question arises: how the emergent symmetry and the associated scaling form with two length scales affect the nonequilibrium dynamics in DQCP. In our previous work [99], we studied the imaginary-time relaxation dynamics at the DQCP of the J-Q 3 model. We found that with an ordered initial VBS (Néel) state, the relaxation dynamics of the VBS (Néel) order parameter is controlled by the conventional correlation length ξ, while the dynamics of the Néel (VBS) order parameter is controlled by the con-finement length ξ .…”

Section: Introductionmentioning

confidence: 99%

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Dual dynamic scaling in deconfined quantum criticality

Shu,

Yin

2022

Preprint

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Emergent symmetry is one of the characteristic phenomena in deconfined quantum critical point (DQCP). As its nonequilibrium generalization, the dual dynamic scaling was recently discovered in the nonequilibrium imaginary-time relaxation dynamics in the DQCP of the J-Q3 model. In this work, we study the nonequilibrium imaginary-time relaxation dynamics in the J-Q2 model, which also hosts a DQCP belonging to the same equilibrium universality class. We not only verify the universality of the dual dynamic scaling at the critical point, but also investigate the breakdown and the vestige of the dual dynamic scaling when the tuning parameter is away from the critical point. We also discuss its possible experimental realizations in devices of quantum computers.

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Section: Brief Review Of the Dynamic Scaling In J-q3 Modelsupporting

confidence: 65%

Section: Model and Imaginary-time Relaxation Dynamicsmentioning

confidence: 99%

Section: Model and Imaginary-time Relaxation Dynamicsmentioning

confidence: 99%

Section: Brief Review Of the Dynamic Scaling In J-q3 Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dual dynamic scaling in deconfined quantum criticality

Shu,

Yin

2022

Preprint

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Imaginary-Time Quantum Relaxation Critical Dynamics with Semi-Ordered Initial States

Li¹,

Yin²,

Shu³

2023

Chinese Phys. Lett.

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We explore the imaginary-time relaxation dynamics near quantum critical points with semi-ordered initial states. Different from the case with homogeneous ordered initial states, in which the order parameter $M$ decays homogeneously as $M\propto \tau^{-\beta/\nu z}$, here $M$ depends on the location $x$, showing rich scaling behaviors. Similar to the classical relaxation dynamics with an initial domain wall in Model A, which describes the purely dissipative dynamics, here as the imaginary time evolves, the domain wall expands into an interfacial region with growing size. In the interfacial region, the local order parameter decays as $M\propto \tau^{-\beta_1/\nu z}$, with $\beta_1$ being an additional dynamic critical exponent. Far away from the interfacial region the local order parameter decays as $M\propto \tau^{-\beta/\nu z}$ in the short-time stage, then crosses over to the scaling behavior of $M\propto \tau^{-\beta_1/\nu z}$ when the location $x$ is absorbed in the interfacial region. A full scaling form characterizing these scaling properties is developed. The quantum Ising model in both one and two dimensions are taken as examples to verify the scaling theory. In addition, we find that for the quantum Ising model the scaling function is an analytical function and $\beta_1$ is not an independent exponent.

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Theory of critical phenomena with long-range temporal interaction

Zeng

Zhong

2023

Phys. Scr.

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We systematically develop theories of critical phenomena with memory of a power-law decaying long-range temporal interaction parameterized by a constant $\theta>0$ for a space dimension $d$ both below and above an upper critical dimension $d_c=6-2/\theta$. We first provide more evidences to confirm the previous theory that a dimensional constant $\mathfrak{d}_t$ is demanded to rectify a hyperscaling law among others. Next, for $d<d_c$, we develop a renormalization-group theory to the leading nontrivial order explicitly and to higher orders formally in $\epsilon=d_c-d$ but to zero order in $\varepsilon=\theta-1$ and find that more scaling laws besides the hyperscaling law are broken due to the breaking of the fluctuation-dissipation theorem. Moreover, because dynamics and statics are intimately interwoven, even the static critical exponents involve contributions from the dynamics and hence do not restore the short-range exponents even for $\theta=1$ and the crossover between the short-range and long-range fixed points is discontinuous contrary to the case of long-range spatial interaction. In addition, a new scaling law relating the dynamic critical exponent with the static ones emerges. However, once $\mathfrak{d}_t$ is displaced by a series of $\epsilon$ and $\varepsilon$ such that most values of the critical exponents are changed, all scaling laws are saved again, even though the fluctuation-dissipation theorem keeps violating. Then, for $d\ge d_c$, we develop an effective-dimension theory by carefully discriminating the corrections of both temporal and spatial dimensions and find three different regions with unique properties. All these results show that the dimensional constant $\mathfrak{d}_t$ is the fundamental ingredient of the theories for critical phenomena with memory. However, its value continuously varies with the space dimension and vanishes exactly at $d=4$, reflecting the variation of the amount of the temporal dimension that is transferred to the spatial one with the strength of fluctuations. Moreover, special finite-size scaling ubiquitously appears except for $d=d_{c0}$

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Nonequilibrium Dynamics of Deconfined Quantum Critical Point in Imaginary Time

Cited by 9 publications

References 80 publications

Dual dynamic scaling in deconfined quantum criticality

Dual dynamic scaling in deconfined quantum criticality

Imaginary-Time Quantum Relaxation Critical Dynamics with Semi-Ordered Initial States

Theory of critical phenomena with long-range temporal interaction

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