Neural-network quantum state study of the long-range antiferromagnetic Ising chain

• URL: http://arxiv.org/abs/2308.09709v3
• Date: Thu, 13 Jun 2024 05:55:37 GMT
• Title: Neural-network quantum state study of the long-range antiferromagnetic Ising chain
• Authors: Jicheol Kim, Dongkyu Kim, Dong-Hee Kim,
• Abstract summary: We investigate quantum phase transitions in the transverse field Ising chain with algebraically decaying long-range (LR) antiferromagnetic interactions. We find that the universal ratio of the SR limit does not hold for $alpha_mathrmLR 2$, implying a deviation in the criticality.
• Score: 0.771303749110121
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate quantum phase transitions in the transverse field Ising chain with algebraically decaying long-range (LR) antiferromagnetic interactions using the variational Monte Carlo method with the restricted Boltzmann machine employed as a trial wave function ansatz. First, we measure the critical exponents and the central charge through the finite-size scaling analysis, verifying the contrasting observations in the previous tensor network studies. The correlation function exponent and the central charge deviate from the short-range (SR) Ising values at a small decay exponent $\alpha_\mathrm{LR}$, while the other critical exponents examined are very close to the SR Ising exponents regardless of $\alpha_\mathrm{LR}$ examined. However, in the further test of the critical Binder ratio, we find that the universal ratio of the SR limit does not hold for $\alpha_\mathrm{LR} < 2$, implying a deviation in the criticality. On the other hand, we find evidence of the conformal invariance breakdown in the conformal field theory (CFT) test of the correlation function. The deviation from the CFT description becomes more pronounced as $\alpha_\mathrm{LR}$ decreases, although a precise breakdown threshold is yet to be determined.

Related papers

• Monitored interacting Dirac fermions [0.0]
  We analytically study interacting Dirac fermions under weak local particle number measurements. This system maps to a bosonic replica field theory, analyzed via the renormalization group.
  arXiv  Detail & Related papers  (2025-02-04T19:00:04Z)
• A Unified Analysis for Finite Weight Averaging [50.75116992029417]
  Averaging iterations of Gradient Descent (SGD) have achieved empirical success in training deep learning models, such as Weight Averaging (SWA), Exponential Moving Average (EMA), and LAtest Weight Averaging (LAWA) In this paper, we generalize LAWA as Finite Weight Averaging (FWA) and explain their advantages compared to SGD from the perspective of optimization and generalization.
  arXiv  Detail & Related papers  (2024-11-20T10:08:22Z)
• Convergence Rate Analysis of LION [54.28350823319057]
  LION converges iterations of $cal(sqrtdK-)$ measured by gradient Karush-Kuhn-T (sqrtdK-)$. We show that LION can achieve lower loss and higher performance compared to standard SGD.
  arXiv  Detail & Related papers  (2024-11-12T11:30:53Z)
• Highly complex novel critical behavior from the intrinsic randomness of quantum mechanical measurements on critical ground states -- a controlled renormalization group analysis [0.0]
  We consider the effects of weak measurements on the quantum critical ground state of the one-dimensional tricritical and critical quantum Ising model. By employing a controlled renormalization group analysis we find that each problem exhibits highly complex novel scaling behavior.
  arXiv  Detail & Related papers  (2024-09-03T17:59:04Z)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations [0.0]
  We study the ferromagnetic transverse-field Ising model with quenched disorder at $T = 0$ in one and two dimensions. The emphasis on effective zero-temperature simulations resolves several inconsistencies in existing literature.
  arXiv  Detail & Related papers  (2024-03-08T11:20:42Z)
• Tunable quantum criticality and pseudocriticality across the fixed-point annihilation in the anisotropic spin-boson model [0.26107298043931204]
  We study the nontrivial renormalization-group scenario of fixed-point annihilation in spin-boson models. We find a tunable transition between two localized phases that can be continuous or strongly first-order. We also find scaling behavior at the symmetry-enhanced first-order transition, for which the inverse correlation-length exponent is given by the bath exponent.
  arXiv  Detail & Related papers  (2024-03-04T19:00:07Z)
• Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency [53.90687548731265]
  We study optimal procedures for estimating a linear functional based on observational data. For any convex and symmetric function class $mathcalF$, we derive a non-asymptotic local minimax bound on the mean-squared error.
  arXiv  Detail & Related papers  (2023-01-16T02:57:37Z)
• SU(2)-Symmetric Spin-Boson Model: Quantum Criticality, Fixed-Point Annihilation, and Duality [0.582519087605215]
  We present high-accuracy quantum Monte Carlo results for the SU(2)-symmetric $S=1/2$ spin-boson (or Bose-Kondo) model. Using a detailed scaling analysis, we provide direct numerical evidence for the collision and annihilation of two RG fixed points at $sast = 0.6540(2)$.
  arXiv  Detail & Related papers  (2022-03-04T19:00:19Z)
• Optimal policy evaluation using kernel-based temporal difference methods [78.83926562536791]
  We use kernel Hilbert spaces for estimating the value function of an infinite-horizon discounted Markov reward process. We derive a non-asymptotic upper bound on the error with explicit dependence on the eigenvalues of the associated kernel operator. We prove minimax lower bounds over sub-classes of MRPs.
  arXiv  Detail & Related papers  (2021-09-24T14:48:20Z)
• On Linear Stochastic Approximation: Fine-grained Polyak-Ruppert and Non-Asymptotic Concentration [115.1954841020189]
  We study the inequality and non-asymptotic properties of approximation procedures with Polyak-Ruppert averaging. We prove a central limit theorem (CLT) for the averaged iterates with fixed step size and number of iterations going to infinity.
  arXiv  Detail & Related papers  (2020-04-09T17:54:18Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.