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Physical review. B./Physical review. B

Mott glass and criticality in an S = 1 2 bilayer Heisenberg model with interlayer bond dilution

K. J. Li, Han-Qing Wu, Dao‐Xin Yao

Published Nov 8, 2025• 0 citations
Publisher

Abstract

We employ the stochastic series expansion quantum Monte Carlo method to investigate the $S=1/2$ antiferromagnetic Heisenberg model on a bilayer square lattice with diluted interlayer couplings. Both regular and random dilution patterns are considered. In systems with regular dilution, tuning the interlayer interaction drives a quantum phase transition from a N\'eel-ordered phase to a quantum disordered phase, consistent with the $O(3)$ universality class. In contrast, random dilution gives rise to a two-step transition: from the N\'eel phase to an intermediate Mott glass (MG) phase, followed by a transition to the quantum disordered phase. Within the MG phase, the uniform magnetic susceptibility exhibits a stretched-exponential temperature dependence ${\ensuremath{\chi}}_{u}\ensuremath{\sim}exp(\ensuremath{-}b/{T}^{\ensuremath{\alpha}}), 0<\ensuremath{\alpha}<1$. At the N\'eel-to-glass transition, the quenched disorder modifies the critical exponents in a manner consistent with the Harris criterion. These findings provide new insights into disorder-driven quantum phase transitions and the emergence of glassy phases in diluted bilayer quantum magnets.

DOI
10.1103/8wbp-xxz1

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We employ the stochastic series expansion quantum Monte Carlo method to investigate the S=1/2S=1/2S=1/2 antiferromagnetic Heisenberg model on a bilayer square lattice with diluted interlayer couplings. Both regular and random dilution patterns are considered. In systems with regular dilution, tuning the interlayer interaction drives a quantum phase transition from a N'eel-ordered phase to a quantum disordered phase, consistent with the O(3)O(3)O(3) universality class. In contrast, random dilution gives rise to a two-step transition: from the N'eel phase to an intermediate Mott glass (MG) phase, followed by a transition to the quantum disordered phase. Within the MG phase, the uniform magnetic susceptibility exhibits a stretched-exponential temperature dependence \ensuremathχu\ensuremath∼exp(\ensuremath−b/T\ensuremathα),0<\ensuremathα<1{\ensuremath{\chi}}_{u}\ensuremath{\sim}exp(\ensuremath{-}b/{T}^{\ensuremath{\alpha}}), 0<\ensuremath{\alpha}<1\ensuremathχu​\ensuremath∼exp(\ensuremath−b/T\ensuremathα),0<\ensuremathα<1. At the N'eel-to-glass transition, the quenched disorder modifies the critical exponents in a manner consistent with the Harris criterion. These findings provide new insights into disorder-driven quantum phase transitions and the emergence of glassy phases in diluted bilayer quantum magnets.
We use quantum Monte Carlo simulations to study a dimer-diluted S = 1/2 Heisenberg model on a bilayer square lattice with intralayer interaction J 1 and interlayer interaction J 2 . Below the classical percolation threshold p c , the system has three phases reachable by tuning the interaction ratio g = J 2 / J 1 : a Néel ordered phase, a gapless quantum glass phase, and a gapped quantum paramagnetic phase. We present the ground-state phase diagram in the plane of dilution p and interaction ratio g . The quantum glass phase is certified to be of the gapless Mott glass type, having a uniform susceptibility vanishing at zero temperature T and following a stretched exponential form at T > 0; χ u exp(- b / T α ) with α < 1. At the phase transition point from Neel ordered to Mott glass, we find that the critical exponents are different from those of the clean system described by the standard O (3) universality class in 2+1 dimensions.
We use quantum Monte Carlo simulations to study a disordered S=1/2S=1/2S=1/2 Heisenberg quantum spin model with three different nearest-neighbor interactions, ${J}_{1}\ensuremath{\le}{J}_{2}\ensuremath{\le}{J}_{3}$, on the square lattice. We consider the regime in which J1{J}_{1}J1​ represents weak bonds, and J2{J}_{2}J2​ and J3{J}_{3}J3​ correspond to two kinds of stronger bonds (dimers) which are randomly distributed on columns forming coupled two-leg ladders. When increasing the average intradimer coupling (J2+J3)/2({J}_{2}+{J}_{3})/2(J2​+J3​)/2, the system undergoes a N\'eel to quantum glass transition of the ground state and later a second transition into a quantum paramagnet. The quantum glass phase is of the gapless Mott glass type (i.e., in boson language it is incompressible at temperature T=0T=0T=0), and we find that the temperature dependence of the uniform magnetic susceptibility follows the stretched exponential form $\ensuremath{\chi}\ensuremath{\sim}exp(\ensuremath{-}b/{T}^{\ensuremath{\alpha}})$, with $0<\ensuremath{\alpha}<1$. At the N\'eel-glass transition, we observe the standard O(3) critical exponents, which implies that the Harris criterion for the relevance of the disorder is violated in this system.
By developing a cluster sampling of the stochastic series expansion quantum Monte Carlo method, we investigate a spin-12\frac{1}{2}21​ model on a bilayer square lattice with intralayer ferromagnetic (FM) Ising coupling and interlayer antiferromagnetic Heisenberg interaction. The continuous quantum phase transition which occurs at gc=3.045(2){g}_{c}=3.045(2)gc​=3.045(2) between the FM Ising phase and the dimerized phase is studied via large-scale simulations. From analysis of the critical exponents we show that this phase transition belongs to the (2+12+12+1)-dimensional Ising universality class. In addition, the quantum entanglement is strong between the two layers, especially in the dimerized phase. The effective Hamiltonian of a single layer seems like a transverse-field Ising model. However, we found that the quantum entanglement Hamiltonian is a pure classical Ising model without any quantum fluctuations. Furthermore, we give a more general explanation about how a classical entanglement Hamiltonian emerges.
The S = 1/2 Heisenberg model is considered on bilayer and single-layer square lattices with couplings J1, J2, with each spin belonging to one J2-coupled dimer. A transition from a Néel to disordered ground state occurs at a critical value of g = J2/J1. The systems are here studied at their dimer-dilution percolation points p*. The multicritical point (g*,p*) previously found for the bilayer is not reproduced for the single layer. Instead, there is a line of critical points (g < g*, p*) with continuously varying exponents. The uniform magnetic susceptibility diverges as T(-alpha) with alpha element of [1/2,1]. This unusual behavior is attributed to an effective free-moment density approximately T(1-alpha). The susceptibility of the bilayer is not divergent but exhibits remarkably robust quantum-critical scaling.
The three-dimensional quenched random bond diluted $({J}_{1}\ensuremath{-}{J}_{2})$ quantum Heisenberg antiferromagnet is studied on a simple-cubic lattice. Using extensive stochastic series expansion quantum Monte Carlo simulations, we perform very long runs for an $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$ lattice up to L=48L=48L=48. By employing a standard finite-size scaling method, the numerical values of the N\'eel temperature are determined with high precision as a function of the coupling ratio r=J2/J1r={J}_{2}/{J}_{1}r=J2​/J1​. Based on the estimated critical exponents, we find that the critical behavior of the considered model belongs to the pure classical three-dimensional O(3)O(3)O(3) Heisenberg universality class.
We present Monte Carlo simulations of a two-dimensional bilayer quantum Heisenberg antiferromagnet with random dimer dilution. In contrast with exotic scaling scenarios found in other random quantum systems, the quantum phase transition in this system is characterized by a finite-disorder fixed point with power-law scaling. After accounting for corrections to scaling, with a leading irrelevant exponent of omega approximately 0.48, we find universal critical exponents z=1.310(6) and nu=1.16(3). We discuss the consequences of these findings and suggest new experiments.