arXiv subjects

Yuchen Meng

Publications and source records attributed to Yuchen Meng.

6 recordsLinked to original sources

arXiv2026

Spontaneous Parity Breaking in Quantum Antiferromagnets on the Triangular Lattice

Frustration on the triangular lattice has long been a source of intriguing and often debated phases in many-body systems. Although symmetry analysis has been employed, the role of the seemingly trivial parity symmetry has received little attention. In this work, we show that phases induced by frustration are systematically shaped by an implicit rule of thumb associated with spontaneous parity breaking. This principle enables us to anticipate and rationalize the regimes and conditions under which nontrivial phases emerge. For the spin-$S$ antiferromagnetic XXZ model, we demonstrate that a controversial parity-broken phase appears only at intermediate values of $S$. In bilayer systems, enhanced frustration leads to additional phases, such as supersolids, whose properties can be classified by their characteristic parity features. Benefiting from our improved tensor network contraction techniques, we confirm these results through large-scale tensor-network calculations. This study offers an alternative viewpoint and a systematic approach for examining the interplay between spin, symmetry, and frustration in many-body systems.

cond-mat.str-el↗

arXiv2025

Topological Feature of Real-time Fisher Zeros

There are numerous methods to characterize topology and its boundary zero modes, yet their statistical mechanical properties have not received as much attention as other approaches. Here, we investigate the Fisher zeros and thermofield dynamics of topological models, revealing that boundary zero modes can be described by an overlooked real-time Fisher zero pairing effect. This effect is validated in the Su-Schrieffer-Heeger model and the Kitaev chain model, with the latter exhibiting a Fisher zero braiding picture. Topological zero modes exhibit robustness even when non-Hermiticity is introduced into the system and display characteristics of imaginary-time crystals when the energy eigenvalues are complex. We further examine the real-time Fisher zeros of the one-dimensional transverse field Ising model, which maps to the Kitaev chain. We present a fractal picture of the Fisher zeros, illustrating how interactions eliminate topology. The mechanism of zero-pairing provides a natural statistical mechanical approach to understanding the connection between topology and many-body physics.

cond-mat.str-el↗

arXiv2025

Detecting Many-Body Scars from Fisher Zeros

The far-from-equilibrium dynamics of certain interacting quantum systems still defy precise understanding. One example is the so-called quantum many-body scars (QMBSs), where a set of energy eigenstates evade thermalization to give rise to long-lived oscillations. Despite the success of viewing scars from the perspectives of symmetry, commutant algebra, and quasiparticles, it remains a challenge to elucidate the mechanism underlying all QMBS and to distinguish them from other forms of ergodicity breaking. In this work, we introduce an alternative route to detect and diagnose QMBS based on Fisher zeros, i.e., the patterns of zeros of the analytically continued partition function $Z$ on the complex $\beta$ (inverse temperature) plane. For systems with scars, a continuous line of Fisher zeros will appear off the imaginary $\beta$ axis and extend upward, separating the $\beta$ plane into regions with distinctive thermalization behaviors. This conjecture is motivated from interpreting the complex $Z$ as the return amplitude of the thermofield double state, and it is validated by analyzing two models with QMBS, the $\bar{P}X\bar{P}$ model and the Ising chain in external fields. These models also illustrate the key difference between QMBS and strong ergodicity breaking including their distinctive renormalization group flows on the complex $\beta$ plane. This ``statistical mechanics" approach places QMBS within the same framework of thermal and dynamical phase transitions. It has the advantage of spotting scars without exhaustively examining each individual quantum state.

cond-mat.str-el↗

arXiv2024

Exact Fisher zeros and thermofield dynamics across a quantum critical point

By setting the inverse temperature $\beta$ loose to occupy the complex plane, Fisher showed that the zeros of the complex partition function $Z$, if approaching the real $\beta$ axis, reveal a thermodynamic phase transition. More recently, Fisher zeros were used to mark the dynamical phase transition in quench dynamics. It remains unclear, however, how Fisher zeros can be employed to better understand quantum phase transitions or the non-unitary dynamics of open quantum systems. Here we answer this question by a comprehensive analysis of the analytically continued one-dimensional transverse field Ising model. We exhaust all the Fisher zeros to show that in the thermodynamic limit they congregate into a remarkably simple pattern in the form of continuous open or closed lines. These Fisher lines evolve smoothly as the coupling constant is tuned, and a qualitative change identifies the quantum critical point. By exploiting the connection between $Z$ and the thermofield double states, we obtain analytical expressions for the short- and long-time dynamics of the survival amplitude, including its scaling behavior at the quantum critical point. We point out $Z$ can be realized and probed in monitored quantum circuits. The exact analytical results are corroborated by the numerical tensor renormalization group. We further show that similar patterns of Fisher zeros also emerge in other spin models. Therefore, the approach outlined may serve as a powerful tool for interacting quantum systems.

cond-mat.str-el↗

arXiv2024

Many-body computing on Field Programmable Gate Arrays

A new implementation of many-body calculations is of paramount importance in the field of computational physics. In this study, we leverage the capabilities of Field Programmable Gate Arrays (FPGAs) for conducting quantum many-body calculations. Through the design of appropriate schemes for Monte Carlo and tensor network methods, we effectively utilize the parallel processing capabilities provided by FPGAs. This has resulted in a tenfold speedup compared to CPU-based computation for a Monte Carlo algorithm. By using a supercell structure and simulating the FPGA architecture on a CPU with High-Level Synthesis, we achieve $O(1)$ scaling for the time of one sweep, regardless of the overall system size. We also demonstrate, for the first time, the utilization of FPGA to accelerate a typical tensor network algorithm for many-body ground state calculations. Additionally, we show that the current FPGA computing acceleration is on par with that of multi-threaded GPU parallel processing. Our findings unambiguously highlight the significant advantages of hardware implementation and pave the way for novel approaches to many-body calculations.

cond-mat.str-el↗

arXiv2023

A note on cube-free problems

Eberhard and Pohoata conjectured that every $3$-cube-free subset of $[N]$ has size less than $2N/3+o(N)$. In this paper we show that if we replace $[N]$ with $\mathbb{Z}_N$ the upper bound of $2N/3$ holds, and the bound is tight when $N$ is divisible by $3$ since we have $A=\{a\in \mathbb{Z}_N:a\equiv 1,2\pmod{3}\}.$ Inspired by this observation we conjecture that every $d$-cube-free subset of $\mathbb{Z}_N$ has size less than $(d-1)N/d$ where $N$ is divisible by $d$, and we show the tightness of this bound by providing an example $B=\{b\in\mathbb{Z}_N:b\equiv 1,2,\ldots,d-1\pmod{d}\}$. We prove the conjecture for several interesting cases, including when $d$ is the smallest prime factor of $N$, or when $N$ is a prime power. We also discuss some related issues regarding $\{x,dx\}$-free sets and $\{x,2x,\ldots,dx\}$-free sets. A main ingredient we apply is to arrange all the integers into some square matrix, with $m=d^s\times l$ having the coordinate $(s+1,l-\lfloor l/d\rfloor)$. Here $d$ is a given integer and $l$ is not divisible by $d$.

math.CO↗