Random Phase Product Sate for Canonical Ensemble

• URL: http://arxiv.org/abs/2006.14459v1
• Date: Thu, 25 Jun 2020 14:53:48 GMT
• Title: Random Phase Product Sate for Canonical Ensemble
• Authors: Toshiaki Iitaka
• Abstract summary: The RPPS method is an extension of the method of random phase state for full Hilbert space representation. The validity of the method is confirmed by comparing the average energy of N-site antiferromagnetic spin-1/2 Heisenberg chain model with open boundary conditions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Method of random phase product state (RPPS) is proposed to calculate canonical ensemble average of quantum systems described with matrix product states and also with tensor network states in general. The RPPS method is an extension of the method of random phase state for full Hilbert space representation. The validity of the method is confirmed by comparing the average energy of N-site antiferromagnetic spin-1/2 Heisenberg chain model with open boundary conditions with the result of direct method (for up to N=14) and minimally entangled typical thermal state (METTS) method (for N=100). Numerical advantages of the RPPS such as parallelization, combined calculation of thermal averages at different temperatures, parameters for controlling error are discussed. View point of self-averaging for the super-convergence of random state method is emphasized in addition to that of typicality.

Related papers

• Semiclassical approximation of the Wigner function for the canonical ensemble [0.0]
  Weyl-Wigner representation of quantum mechanics allows one to map the density operator in a function in phase space. We approximate this quantum phase space representation of the canonical density operator for general temperatures. A numerical scheme which allows us to apply the approximation for a broad class of systems is also developed.
  arXiv  Detail & Related papers  (2023-07-31T12:44:23Z)
• A blob method method for inhomogeneous diffusion with applications to multi-agent control and sampling [0.6562256987706128]
  We develop a deterministic particle method for the weighted porous medium equation (WPME) and prove its convergence on bounded time intervals. Our method has natural applications to multi-agent coverage algorithms and sampling probability measures.
  arXiv  Detail & Related papers  (2022-02-25T19:49:05Z)
• Taming Quantum Noise for Efficient Low Temperature Simulations of Open Quantum Systems [4.866728358750297]
  We introduce an effective treatment of quantum noise in frequency space by systematically clustering higher order Matsubara poles equivalent to an optimized rational decomposition. This leads to an elegant extension of the HEOM to arbitrary temperatures and very general reservoirs in combination with efficiency, high accuracy and long-time stability. As one highly non-trivial application, for the sub-ohmic spin-boson model at vanishing temperature the Shiba relation is quantitatively verified which predicts the long-time decay of correlation functions.
  arXiv  Detail & Related papers  (2022-02-08T18:46:11Z)
• Non-Markovian Stochastic Schr\"odinger Equation: Matrix Product State Approach to the Hierarchy of Pure States [65.25197248984445]
  We derive a hierarchy of matrix product states (HOMPS) for non-Markovian dynamics in open finite temperature. The validity and efficiency of HOMPS is demonstrated for the spin-boson model and long chains where each site is coupled to a structured, strongly non-Markovian environment.
  arXiv  Detail & Related papers  (2021-09-14T01:47:30Z)
• Linear Convergence of Entropy-Regularized Natural Policy Gradient with Linear Function Approximation [30.02577720946978]
  We establish finite-time convergence analyses of entropy-regularized NPG with linear function approximation. We prove that entropy-regularized NPG exhibits emphlinear convergence up to a function approximation error.
  arXiv  Detail & Related papers  (2021-06-08T04:30:39Z)
• Exact thermal properties of free-fermionic spin chains [68.8204255655161]
  We focus on spin chain models that admit a description in terms of free fermions. Errors stemming from the ubiquitous approximation are identified in the neighborhood of the critical point at low temperatures.
  arXiv  Detail & Related papers  (2021-03-30T13:15:44Z)
• Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach [51.819912248960804]
  We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system.
  arXiv  Detail & Related papers  (2021-03-12T13:16:18Z)
• Matrix product state approach for a quantum system at finite temperatures using random phases and Trotter gates [0.0]
  We develop a numerical method for simulating quantum many-body systems at finite temperatures without importance sampling. Our method is an extension of the random phase product state (RPPS) approach introduced recently.
  arXiv  Detail & Related papers  (2021-03-08T02:28:24Z)
• The Connection between Discrete- and Continuous-Time Descriptions of Gaussian Continuous Processes [60.35125735474386]
  We show that discretizations yielding consistent estimators have the property of invariance under coarse-graining' This result explains why combining differencing schemes for derivatives reconstruction and local-in-time inference approaches does not work for time series analysis of second or higher order differential equations.
  arXiv  Detail & Related papers  (2021-01-16T17:11:02Z)
• 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)
• Local optimization on pure Gaussian state manifolds [63.76263875368856]
  We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm. The method is based on notions of descent gradient attuned to the local geometry. We use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.
  arXiv  Detail & Related papers  (2020-09-24T18:00:36Z)

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.