Efficient Simulation of Low Temperature Physics in One-Dimensional Gapless Systems

• URL: http://arxiv.org/abs/2309.02519v2
• Date: Mon, 29 Jul 2024 19:12:06 GMT
• Title: Efficient Simulation of Low Temperature Physics in One-Dimensional Gapless Systems
• Authors: Yuya Kusuki, Kotaro Tamaoka, Zixia Wei, Yasushi Yoneta,
• Abstract summary: We discuss the computational efficiency of the finite temperature simulation with the minimally entangled typical thermal states (METTS) We show that METTS provide a significant speedup compared to employing the purification method to analyze thermal equilibrium states at low temperatures in 1D gapless systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We discuss the computational efficiency of the finite temperature simulation with the minimally entangled typical thermal states (METTS). To argue that METTS can be efficiently represented as matrix product states, we present an analytic upper bound for the average entanglement Renyi entropy of METTS for Renyi index $0<q\leq 1$. In particular, for 1D gapless systems described by CFTs, the upper bound scales as $\mathcal{O}(c N^0 \log \beta)$ where $c$ is the central charge and $N$ is the system size. Furthermore, we numerically find that the average Renyi entropy exhibits a universal behavior characterized by the central charge and is roughly given by half of the analytic upper bound. Based on these results, we show that METTS provide a significant speedup compared to employing the purification method to analyze thermal equilibrium states at low temperatures in 1D gapless systems.

Related papers

• High-precision simulation of finite-size thermalizing systems at long times [6.907555940790131]
  We propose a simple and efficient numerical method so that the simulation error is of higher order in $1/N$. This finite-size error scaling is proved by assuming the eigenstate thermalization hypothesis.
  arXiv  Detail & Related papers  (2024-06-08T08:39:21Z)
• A Mean-Field Analysis of Neural Stochastic Gradient Descent-Ascent for Functional Minimax Optimization [90.87444114491116]
  This paper studies minimax optimization problems defined over infinite-dimensional function classes of overparametricized two-layer neural networks. We address (i) the convergence of the gradient descent-ascent algorithm and (ii) the representation learning of the neural networks. Results show that the feature representation induced by the neural networks is allowed to deviate from the initial one by the magnitude of $O(alpha-1)$, measured in terms of the Wasserstein distance.
  arXiv  Detail & Related papers  (2024-04-18T16:46:08Z)
• Temperature fluctuations in mesoscopic systems [0.060433560286877776]
  We study temperature fluctuations in mesoscopic $N$-body systems undergoing non-equilibrium processes. Also, we examine the impact of temperature fluctuations in a finite-size quasi-static Carnot engine.
  arXiv  Detail & Related papers  (2023-09-27T08:38:52Z)
• Ground state preparation with shallow variational warm-start [5.526775342940154]
  This work provides a quantum ground state preparation scheme with shallow variational warm-start to tackle the bottlenecks of current algorithms. We demonstrate the effectiveness of our methods via extensive numerical simulations on spin-$1/2$ Heisenberg models. We extend research on the Hubbard model, demonstrating superior performance compared to the prevalent variational quantum algorithms.
  arXiv  Detail & Related papers  (2023-03-20T15:36:23Z)
• Renormalization group for open quantum systems using environment temperature as flow parameter [0.0]
  We present the $T$-flow renormalization group method, which computes the memory kernel for the density-operator evolution of an open quantum system. We benchmark in the stationary limit, readily accessible in real-time for voltages on the order of the coupling or larger. We analytically show that the short-time dynamics of both local and non-local observables follow a universal temperature-independent behaviour.
  arXiv  Detail & Related papers  (2021-11-14T11:52:27Z)
• Mean-Square Analysis with An Application to Optimal Dimension Dependence of Langevin Monte Carlo [60.785586069299356]
  This work provides a general framework for the non-asymotic analysis of sampling error in 2-Wasserstein distance. Our theoretical analysis is further validated by numerical experiments.
  arXiv  Detail & Related papers  (2021-09-08T18:00:05Z)
• Measurement of the Low-temperature Loss Tangent of High-resistivity Silicon with a High Q-factor Superconducting Resonator [58.720142291102135]
  We present the direct loss tangent measurement of a high-resist intrinsicivity (100) silicon wafer in the temperature range from 70 mK to 1 K. The measurement was performed using a technique that takes advantage of a high quality factor superconducting niobium resonator.
  arXiv  Detail & Related papers  (2021-08-19T20:13:07Z)
• Uhlmann Fidelity and Fidelity Susceptibility for Integrable Spin Chains at Finite Temperature: Exact Results [68.8204255655161]
  We show that the proper inclusion of the odd parity subspace leads to the enhancement of maximal fidelity susceptibility in the intermediate range of temperatures. The correct low-temperature behavior is captured by an approximation involving the two lowest many-body energy eigenstates.
  arXiv  Detail & Related papers  (2021-05-11T14:08:02Z)
• Role of topology in determining the precision of a finite thermometer [58.720142291102135]
  We find that low connectivity is a resource to build precise thermometers working at low temperatures. We compare the precision achievable by position measurement to the optimal one, which itself corresponds to energy measurement.
  arXiv  Detail & Related papers  (2021-04-21T17:19:42Z)
• Spectral Analysis of Product Formulas for Quantum Simulation [0.0]
  We show that the Trotter step size needed to estimate an energy eigenvalue within precision can be improved in scaling from $epsilon$ to $epsilon1/2$ for a large class of systems. Results partially generalize to diabatic processes, which remain in a narrow energy band separated from the rest of the spectrum by a gap.
  arXiv  Detail & Related papers  (2021-02-25T03:17:25Z)
• Adiabatic Sensing Technique for Optimal Temperature Estimation using Trapped Ions [64.31011847952006]
  We propose an adiabatic method for optimal phonon temperature estimation using trapped ions. The relevant information of the phonon thermal distributions can be transferred to the collective spin-degree of freedom. We show that each of the thermal state probabilities is adiabatically mapped onto the respective collective spin-excitation configuration.
  arXiv  Detail & Related papers  (2020-12-16T12:58:08Z)

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.