Worm-type Monte Carlo Simulations Of Many-body Lattice Critical Systems

Lattice models are crucial platforms for the study of phase transitions and have a close relationship with several real physical systems.In this thesis,we study the phase transitions and critical phenomena of lattice models utilizing high-efficiency worm Monte Carlo methods.We explore the extraordinary-log universality classes of surface and interface systems,the surface and interface criticality of an incommensurate Villain model,and the spin-ice phases of hard-core bosons on the breathing pyrochlore lattice.In the Introduction,first,we briefly review phase transitions and critical behaviors.We outline the surface and interface criticality.We then introduce many-body lattice systems that will be mentioned in this thesis,which include the classical Villain and quantum Bose-Hubbard models.Finally,we introduce the Monte Carlo method which is an efficient numerical methodology based on random sampling and known as an important method for the study of many-body lattice critical systems.In the second chapter,we introduce the principles and formulations of worm-type Monte Carlo algorithms.In the subsequent chapters,we report the studies that include:(1)By designing a worm-type classical Monte Carlo algorithm,we study the surface criticality of Villain model and explore the classical-quantum correspondence of surface criticality.Using large-scale Monte Carlo simulations and finite-size scaling theory,we determine the thermal and magnetic renormalization exponents of the special transition,which are close to the recent estimates from discrete spin models.For the regime of strong surface coupling,we determine the logarithmic scaling behaviors of two-point correlation and superfluid stiffness,and obtain the estimates of critical exponent and renormalization-group parameter.On this basis,we reveal the existence of extraordinary-log universality class and confirm the scaling relation of extraordinary-log critical theory.(2)Utilizing a worm-type quantum Monte Carlo algorithm,we study the edge criticality of a two-dimensional Bose-Hubbard model.On top of an insulating bulk,with the enhancement of edge hopping strength,the open edges experience a Kosterlitz-Thouless-like transition and fall into the superfluid phase.At the bulk critical point,the open edges may exhibit the special,ordinary,and extraordinary critical phases.In the extraordinary critical phase,logarithms are involved in the finite-size scaling of two-point correlation and superfluid stiffness,which indicates a classical-quantum correspondence of extraordinary-log universality.Based on the aforementioned results and the development of quantum-emulating techniques for lattice bosonic systems,we expect that the extraordinary-log critical phase might be experimentally realized.(3)By designing a worm-type classical Monte Carlo algorithm,we study the interface criticality of three-dimensional Villain model.We obtain convincing evidence for the existence of extraordinary-log criticality in an interface system and reveal the ordinary critical phase and Kosterlitz-Thouless-like transition.For the extraordinary-log critical phase,we systematically determine the universal estimates of critical exponent and renormalization-group parameter,and confirm the scaling relation of the extraordinary-log critical theory.In particular,the extraordinary-log criticality in the interface system belongs to a new universality class.(4)To bridge surface and interface critical behaviors,we design a three-dimensional Villain model that has a pair of nearest-neighbor plane defects,and provide a worm-type Monte Carlo algorithm.On the basis of extensive Monte Carlo simulations,we find the parameter regime for the extraordinary-log critical phase and obtain the estimates of the critical exponent (?)and the renormalization-group parameter.We find a threshold value J_c for the coupling strength J between the plane defects:for J>J_c and J<J_c,the values of((?),α)are close to the corresponding exponents of interface and surface criticality,respectively.Therefore,by tuning the coupling between the plane defects,the evolution of extraordinary-log universality class can be realized.(5)Using a worm-type classical Monte Carlo algorithm,we study the three-dimensional incommensurate Villain model and explore the surface and interface critical behaviors.By means of numerical simulations and finite-size scaling analyses,we obtain a precise estimate of bulk critical point,which significantly surpasses the precision in the literature.At the precise bulk critical point,we simulate the surface and interface of the model and utilize finite-size scaling to explore relevant critical behaviors.In the strong coupling regime,the surface and interface exhibit Kosterlitz-Thouless-like critical behaviors,where the anomalous dimension of correlation function varies continuously upon changing coupling strength.(6)Utilizing a worm-type quantum Monte Carlo algorithm,we study the interacting hard-core bosonic systems on the breathing pyrochlore lattice.First,we construct the complete ground-state phase diagram,which contains the antiferromagnetic,paramagnetic and spin-ice phases.On this basis,by tuning the degree of asymmetry for the breathing pyrochlore lattice,we explore the thermodynamic critical behaviors of spin-ice phases.By analyzing the temperature dependence of entropy and specific heat,we distinguish classical and quantum spin-ice phases,and further reveal the transformation in between.We find that the transformation temperature can be enhanced by increasing the degree of asymmetry.Therefore,we present a scheme to improve the temperature for realizing quantum spin ice in experiments,and lay the foundation for future studies of surface and interface criticality in spin ice.To sum up,we adopt worm-type Monte Carlo simulations to study the surface and interface criticality of classical and quantum lattice many-body systems.Our study provides a novel host for extraordinary-log criticality and deepens the understanding of surface and interface criticality in typical systems.Moreover,we study the spin-ice phases of hard-core bosonic systems on the breathing pyrochlore lattice and present a theoretical proposal to improve the temperature for realizing quantum spin-ice phase.This thesis is helpful for understanding the exotic phase transitions and critical phenomena in many-body systems,and could be a reference for designing new Monte Carlo algorithms.