Snapshot spectra in the world-line quantum Monte Carlo for one-dimensional quantum spin systems

Abstract

We introduce a snapshot density matrix and snapshot spectrum for world-line (WL) quantum Monte Carlo simulations, by integrating out the continuous-imaginary-time index of WL snapshots. For the transverse-field Ising chain, we reveal fundamental properties of the snapshot spectrum as follows. (i) In the ordered phase, the isolated peak corresponding to the maximum eigenvalue appears, indicating the classical nature of WL configurations. (ii) In the disordered phase, the spectrum converges to the dome-like distribution characterized by an effective aspect ratio of the snapshots. (iii) At the critical point, the power-law distribution is observed with an appropriate scaling analysis of the fixed aspect ratio. For the XXZ chain, we also obtain numerical results consistent with the above properties. In addition, the representation-basis dependence of the snapshot spectrum is also discussed.

10 pages, 16 figures

References in corpus (5)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Tensor renormalization group approach to 2D classical lattice models
• Snapshot spectrum and critical phenomenon for two-dimensional classical spin systems
• Entropy of Factorized Snapshot Data for Two-Dimensional Classical Spin Models
• Definitions of entanglement entropy of spin systems in the valence-bond basis

Cited by in corpus (1)

• Lattice Unruh effect and world-line entanglement for the XXZ chain