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Dynamical spin structure factor from a variational Monte Carlo perspective

Federico Becca

Bulletin of the American Physical SocietyMar 4, 20190 citations

Dynamic structure factor from real time evolution and exact correction vectors with matrix product states

Ling Wang, Hai‐Qing Lin

We propose two complimentary numerical methods for rigorous computation of dynamic structure factor at zero temperature. One solution is to solve Schrodinger equation using time dependent variational principle (TDVP) with matrix product states (MPSs) proposed by Haegeman el al. [Physical Review B 94, 165116], and Fourier transform correlation functions in time to frequency domain. Another way is to directly compute the transition rate between the ground state and several low lying momentum eigenstates that are accessed using MPSs method amended with momentum filtering process. We benchmark both methods on a spin-1/2 Antiferromagnetic (AF) Heisenberg chain with periodic boundary condition. With finite size scaling analysis, the asymptotic line shape as a function of ω can be reproduced at various momentum k with both methods.We propose two complimentary numerical methods for rigorous computation of dynamic structure factor at zero temperature. One solution is to solve Schrodinger equation using time dependent variational principle (TDVP) with matrix product states (MPSs) proposed by Haegeman el al. [Physical Review B 94, 165116], and Fourier transform correlation functions in time to frequency domain. Another way is to directly compute the transition rate between the ground state and several low lying momentum eigenstates that are accessed using MPSs method amended with momentum filtering process. We benchmark both methods on a spin-1/2 Antiferromagnetic (AF) Heisenberg chain with periodic boundary condition. With finite size scaling analysis, the asymptotic line shape as a function of ω can be reproduced at various momentum k with both methods.

arXiv:1901.07751Jan 23, 20192 citations

A Monte Carlo Time-Dependent Variational Principle

Fabian Transchel, Ashley Milsted, Tobias J. Osborne

We generalize the Time-Dependent Variational Principle (TDVP) to dissipative systems using Monte Carlo methods, allowing the application of existing variational classes for pure states, such as Matrix Product States (MPS), to the simulation of Lindblad master equation dynamics. The key step is to use sampling to approximately solve the Fokker-Planck equation derived from the Lindblad generators. An important computational advantage of this method, compared to other variational approaches to mixed state dynamics, is that it is "embarrassingly parallel".We generalize the Time-Dependent Variational Principle (TDVP) to dissipative systems using Monte Carlo methods, allowing the application of existing variational classes for pure states, such as Matrix Product States (MPS), to the simulation of Lindblad master equation dynamics. The key step is to use sampling to approximately solve the Fokker-Planck equation derived from the Lindblad generators. An important computational advantage of this method, compared to other variational approaches to mixed state dynamics, is that it is "embarrassingly parallel".

arXiv:1411.5546Nov 20, 20145 citations

Dynamical structure factor of frustrated spin models: a variational Monte Carlo approach

Federico Becca, Francesco Ferrari, Sandro Sorella

Bulletin of the American Physical SocietyMar 8, 20180 citations

Splitting the local Hilbert space: Matrix product state based approach to large local dimensions

Naushad Ahmad Kamar, Mohammad F. Maghrebi

A large, or even infinite, local Hilbert space dimension poses a significant computational challenge for simulating quantum systems. In this work, we present a matrix product state (MPS) based method for simulating one-dimensional quantum systems with a large local Hilbert space dimension, an example being bosonic systems with a large on-site population. To this end, we split the local Hilbert space corresponding to one site into two sites, each with a smaller Hilbert space dimension. An advantage of this method is that it can be easily integrated into MPS based techniques such as time-dependent variational principle (TDVP) without changing their standard algorithmic structure. Here, we implement our method using the TDVP to simulate the dynamics of the spin-boson model, a prototypical model of a spin interacting with a large bath of bosonic modes. We benchmark our method against and find excellent agreement with previous studies.A large, or even infinite, local Hilbert space dimension poses a significant computational challenge for simulating quantum systems. In this work, we present a matrix product state (MPS) based method for simulating one-dimensional quantum systems with a large local Hilbert space dimension, an example being bosonic systems with a large on-site population. To this end, we split the local Hilbert space corresponding to one site into two sites, each with a smaller Hilbert space dimension. An advantage of this method is that it can be easily integrated into MPS based techniques such as time-dependent variational principle (TDVP) without changing their standard algorithmic structure. Here, we implement our method using the TDVP to simulate the dynamics of the spin-boson model, a prototypical model of a spin interacting with a large bath of bosonic modes. We benchmark our method against and find excellent agreement with previous studies.

arXiv:2307.16031Physical review. B./Physical review. BAug 8, 20245 citations

Group Approach in Spin Dynamics

V Sinivee

Springer eBooksJan 1, 19790 citations

Computing dynamic spin structure factor using matrix product state method and the time dependent variational principle

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