Quantum Monte Carlo simulations in the trimer basis: first-order transitions and thermal critical points in frustrated trilayer magnets

Abstract

The phase diagrams of highly frustrated quantum spin systems can exhibit first-order quantum phase transitions and thermal critical points even in the absence of any long-ranged magnetic order. However, all unbiased numerical techniques for investigating frustrated quantum magnets face significant challenges, and for generic quantum Monte Carlo methods the challenge is the sign problem. Here we report on a general quantum Monte Carlo approach with a loop-update scheme that operates in any basis, and we show that, with an appropriate choice of basis, it allows us to study a frustrated model of coupled spin-1/2 trimers: simulations of the trilayer Heisenberg antiferromagnet in the spin-trimer basis are sign-problem-free when the intertrimer couplings are fully frustrated. This model features a first-order quantum phase transition, from which a line of first-order transitions emerges at finite temperatures and terminates in a thermal critical point. The trimer unit cell hosts an internal degree of freedom that can be controlled to induce an extensive entropy jump at the quantum transition, which alters the shape of the first-order line. We explore the consequences for the thermal properties in the vicinity of the critical point, which include profound changes in the lines of maxima defined by the specific heat. Our findings reveal trimer quantum magnets as fundamental systems capturing in full the complex thermal physics of the strongly frustrated regime.

arXiv comment27 pages, 10 figures, Resubmission to SciPost

References in corpus (48)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Quantum Monte Carlo with Directed Loops
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Computational Studies of Quantum Spin Systems
• Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• Unusual ordered phases of highly frustrated magnets: a review
• Generalized Directed Loop Method for Quantum Monte Carlo Simulations
• Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model
• Finite size and temperature effects in the AF Heisenberg model
• Critical level crossings and gapless spin liquid in the square-lattice spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet
• Crystals of bound states in the magnetization plateaus of the Shastry-Sutherland model
• Magnetic Exchange Interactions in BaMn2As2: A Case Study of the J1-J2-Jc Heisenberg Model
• Frustrated ferromagnetic spin-1/2 chain in a magnetic field: The phase diagram and thermodynamic properties
• Magnetization plateaux and jumps in a class of frustrated ladders: A simple route to a complex behaviour
• A quantum magnetic analogue to the critical point of water
• The $S=1/2$ Kagome Heisenberg Antiferromagnet Revisited
• Exact Demonstration of Magnetization Pleateaus and First Order Dimer-Néel Phase Transitions in a Modified Shastry-Sutherland Model for SrCu${}_2$(BO${}_3$)${}_2$
• Magnetic characterization of the frustrated three-leg ladder compound [(CuCl2tachH)3Cl]Cl2
• Easing the Monte Carlo sign problem
• Directed Loop Updates for Quantum Lattice Models
• Universal properties of highly frustrated quantum magnets in strong magnetic fields
• Exponent relations at quantum phase transitions, with applications to metallic quantum ferromagnets
• Sign-problem-free Monte Carlo simulation of certain frustrated quantum magnets
• Soliton binding and low-lying singlets in frustrated odd-legged S=1/2 spin tubes
• Vanishing of the negative-sign problem of quantum Monte Carlo simulations in one-dimensional frustrated spin systems
• Thermodynamic properties of the Shastry-Sutherland model from quantum Monte Carlo simulations
• Thermodynamic properties of highly frustrated quantum spin ladders: influence of many-particle bound states
• Emergent Ising degrees of freedom in frustrated two-leg ladder and bilayer $s=1/2$ Heisenberg antiferromagnets
• Spin-Wave Theory and Finite-Size Scaling for the Heisenberg Antiferromagnet
• Cluster representations and the Wolff algorithm in arbitrary external fields
• Finite-temperature order-disorder phase transition in a frustrated bilayer quantum Heisenberg antiferromagnet in strong magnetic fields
• Thermal Critical Points and Quantum Critical End Point in the Frustrated Bilayer Heisenberg Antiferromagnet
• Efficient Quantum Monte Carlo simulations of highly frustrated magnets: the frustrated spin-1/2 ladder
• Stochastic Cluster Series expansion for quantum spin systems
• Simulations of Quantum XXZ Models on Two-Dimensional Frustrated Lattices
• Almost Perfect Frustration in the Dimer Magnet Ba${}_2$CoSi${}_2$O${}_6$Cl${}_2$
• Emergent Bound States and Impurity Pairs in Chemically Doped Shastry-Sutherland System
• Exotic phase diagram of a cluster charging model of bosons on the kagome lattice
• Field-Induced Quantum Phases in Frustrated Spin-Dimer Model: A Sign-Problem-Free Quantum Monte Carlo Study
• Determining QMC simulability with geometric phases
• Valence bond solid and possible deconfined quantum criticality in an extended kagome lattice Heisenberg antiferromagnet
• Quantum cluster algorithm for frustrated Ising models in a transverse field
• Monte Carlo study of the discontinuous quantum phase transition in the transverse-field Ising model on the pyrochlore lattice
• Reduction of the sign problem near $T=0$ in quantum Monte Carlo simulations

Cited by in corpus (18)

• Plaquette Singlet Transition, Magnetic Barocaloric Effect, and Spin Supersolidity in the Shastry-Sutherland Model
• Thermodynamic crossovers in supercritical fluids
• Frustrated magnetism of spin-1/2 Heisenberg diamond and octahedral chains as a statistical-mechanical monomer-dimer problem
• Cavity-renormalized quantum criticality in a honeycomb bilayer antiferromagnet
• Phases of the spin-1/2 Heisenberg antiferromagnet on the diamond-decorated square lattice in a magnetic field
• Thermal first-order phase transitions, Ising critical points, and reentrance in the Ising-Heisenberg model on the diamond-decorated square lattice in a magnetic field
• Spin-half Heisenberg antiferromagnet on a symmetric sawtooth chain: Rotation-invariant Green's functions and high-temperature series
• Thermal critical points from competing singlet formations in fully frustrated bilayer antiferromagnets
• Emergent criticality in fully frustrated quantum magnets
• Magnon, doublon and quarton excitations in 2D S=1/2 trimerized Heisenberg models
• Cluster quantum Monte Carlo study of two-dimensional weakly-coupled frustrated trimer antiferromagnets
• Thermodynamic properties of the macroscopically degenerate tetramer-dimer phase of the spin-1/2 Heisenberg model on the diamond-decorated square lattice
• Liquid-gas analog multicriticality in a frustrated Ising bilayer
• Carlo.jl: A general framework for Monte Carlo simulations in Julia
• Phase transitions in the spin-1/2 Heisenberg antiferromagnet on the dimerized diamond lattice
• Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models
• Magnetization plateaus, spin-canted orders and field-induced transitions in a spin-1/2 Heisenberg antiferromagnet on a distorted diamond-decorated honeycomb lattice
• Advanced measurement techniques in quantum Monte Carlo: The permutation matrix representation approach