Macrostates vs. Microstates in the Classical Simulation of Critical Phenomena in Quench Dynamics of 1D Ising Models

• DOI: 10.48550/arxiv.2310.08567
• Publication Date: 2023-01-01
• Authors: Anupam Mitra; Tameem Albash; Philip Daniel Blo...; Jun Takahashi; Akimasa Miyake; Grant Biedermann; Ivan Deutsch
• Keywords: Critical point (mathematics); Matrix product state

We study the tractability of classically simulating critical phenomena in quench dynamics one-dimensional transverse field Ising models (TFIMs) using highly truncated matrix product states (MPS). focus on two paradigmatic examples: a dynamical quantum phase transition (DQPT) that occurs nonintegrable long-range TFIMs, and infinite-time correlation length integrable nearest-neighbor TFIM when quenched to point. For DQPT, we show order parameters can be efficiently simulated with surprisingly heavy truncation MPS bond dimension. This used reliably extract properties transition, including exponents, even full many-body state is not high fidelity. The long-time near point more sensitive fidelity, generally requires large dimension MPS. Nonetheless, find this still strongly because it extracted from short-time behavior where entanglement low. Our results demonstrate while accurate calculation (microstate) typically intractable due volume-law growth entanglement, precise specification an exact microstate may required phases matter systems (macrostates). also simulation based chaos equilibration models. counterintuitive inverse relationship, whereby local expectation values are most easily approximated for chaotic whose intractable.