Abstract The quantum phase transition between Z 2 plaquette valence bound solid (PVBS) and superfluid (SF) phases on the planar pyrochlore lattice (square ice) is under debate. To gain further insight, here, we focus on the dynamical features of the hard-core Bose–Hubbard model on this lattice and study the excitation spectra by combining stochastic analytic continuation and quantum Monte Carlo simulation. In both PVBS and SF phases, a flat band with bow-tie structure is observed and can be explained by certain symmetries. At the transition point, the spectra turn to be continuous and gapless. A (2+1)-dimensional Abelian–Higgs model with mixed ’t Hooft anomaly is proposed to describe the transition, where the anomaly matching predicts that the deconfinement can exist on the domain walls. From the snapshot of the spin configuration in real space, we found the existence of the domain wall. We also found that the spectrum along a specific path in momentum space from PVBS phase to the transition point can be well described by an XXZ spin chain, and the critical theory of XXZ spin chain matches the anomaly. The two-spinon continuum along this specific path implies additional domain walls (point defect) can emerge in the domain walls (line defect) and take the role of deconfinement at the transition point.
Abstract The quantum phase transition between Z 2 plaquette valence bound solid (PVBS) and superfluid (SF) phases on the planar pyrochlore lattice (square ice) is under debate. To gain further insight, here, we focus on the dynamical features of the hard-core Bose–Hubbard model on this lattice and study the excitation spectra by combining stochastic analytic continuation and quantum Monte Carlo simulation. In both PVBS and SF phases, a flat band with bow-tie structure is observed and can be explained by certain symmetries. At the transition point, the spectra turn to be continuous and gapless. A (2+1)-dimensional Abelian–Higgs model with mixed ’t Hooft anomaly is proposed to describe the transition, where the anomaly matching predicts that the deconfinement can exist on the domain walls. From the snapshot of the spin configuration in real space, we found the existence of the domain wall. We also found that the spectrum along a specific path in momentum space from PVBS phase to the transition point can be well described by an XXZ spin chain, and the critical theory of XXZ spin chain matches the anomaly. The two-spinon continuum along this specific path implies additional domain walls (point defect) can emerge in the domain walls (line defect) and take the role of deconfinement at the transition point.
The quantum phase transition between Z2 plaquette valence bound solid (PVBS) and superfluid (SF) phases on the planar pyrochlore lattice (square ice) is under debate, because the conventional deconfined theory does not support continuous one, but the numerical evidence is still not solid. Here, we propose the system can be effectively described by a 2+1 dimensional Abelian-Higgs model which may host the mixed 't Hooft anomaly, so that the deconfinement can exist on the domain walls at the transition point. To verify it, we study the spin excitation spectra by combining stochastic analytic continuation and quantum Monte Carlo simulation. In both PVBS and SF phases, a flat band with bow-tie structure is observed and can be explained by group theoretic analysis. At the transition point, the spectra turn to be continuous and gapless, which indicates the topological excitations. From the snapshot of the spin configuration in real space, we found the existence of the domain wall in which the symmetries satisfy the anomaly. Meanwhile, a Luttinger liquid like continuum implies additional domain walls (point-defect) can emerge in the domain walls (line-defect) and take the role of deconfinement at transition point, as prediction of mixed 't Hooft anomaly. Our work can build a new bridge between the topological gauge field theory and a strongly correlated system.
We consider the Abelian-Higgs model in 2+1 dimensions with instanton-monopole defects. This model is closely related to the phases of quantum antiferromagnets. In the presence of Z2 preserving monopole operators, there are two confining ground states in the monopole phase, corresponding to the valence bond solid (VBS) phase of quantum magnets. We show that the domain wall carries a 't Hooft anomaly in this case. The anomaly can be saturated by, e.g., charge-conjugation breaking on the wall or by the domain wall theory becoming gapless (a gapless model that saturates the anomaly is SU(2)1 WZW). Either way the fundamental scalar particles (i.e., spinons) which are confined in the bulk are deconfined on the domain wall. This Z2 phase can be realized either with spin-1/2 on a rectangular lattice or spin-1 on a square lattice. In both cases the domain wall contains spin-1/2 particles (which are absent in the bulk). We discuss the possible relation to recent lattice simulations of domain walls in VBS. We further generalize the discussion to Abrikosov-Nielsen-Olsen (ANO) vortices in a dual superconductor of the Abelian-Higgs model in 3+1 dimensions and to the easy-plane limit of antiferromagnets. In the latter case the wall can undergo a variant of the BKT transition (consistent with the anomalies) while the bulk is still gapped. The same is true for the easy-axis limit of antiferromagnets. We also touch upon some analogies to Yang-Mills theory.
We study the quantum spin dynamics of a frustrated XXZ model on a pyrochlore lattice by using large-scale quantum Monte Carlo simulation and stochastic analytic continuation. In the low-temperature quantum spin ice regime, we observe signatures of coherent photon and spinon excitations in the dynamic spin structure factor. As the temperature rises to the classical spin ice regime, the photon disappears from the dynamic spin structure factor, whereas the dynamics of the spinon remain coherent in a broad temperature window. Our results provide experimentally relevant, quantitative information for the ongoing pursuit of quantum spin ice materials.
Dirac fermions in (2 + 1) dimensions with dynamically generated anticommuting SO(3) antiferromagnetic and Z2 Kekul\'e valence-bond solid (KVBS) masses map onto a field theory with a topological $\ensuremath{\theta}$ term. This term provides a mechanism for continuous phase transitions between different symmetry-broken states: topological defects of one phase carry the charge of the other and proliferate at the transition. The $\ensuremath{\theta}$ term implies that a domain wall of the Z2 KVBS order parameter harbors a spin-1/2 Heisenberg chain, as described by a (1 + 1)-dimensional SO(3) nonlinear sigma model with $\ensuremath{\theta}$ term at $\ensuremath{\theta}=\ensuremath{\pi}$. Using pinning fields to stabilize the domain wall, we show that our auxiliary-field quantum Monte Carlo simulations indeed support the emergence of a spin-1/2 chain at the Z2 topological defect. Surprisingly, the consequences of the topological term are seen far from the critical point such that the physics of apparently unrelated model systems are naturally understood by invoking them. This concept can be generalized to higher dimensions where (2 + 1)-dimensional SO(4) or SO(5) theories with topological terms are realized at a domain wall.
Three dimensional frustrated magnets realized in the rare-earth pyrochlores R_2B_2O_7, R=rare-earth ion, B transition metal ion) have attracted much interest since the discovery of spin ice in Ho_2Ti_2O_7 by Harris et al. Since then, a number of interesting phenomena in pyrochlore magnets have been observed and the interest in these systems, from an experimental and theoretical point of view, has nothing but increased. Perhaps the most appealing and unique possibility is that these systems may realize a quantum disordered phase; a so-called quantum spin ice. Theoretically, it has been predicted by Hermele et al. that a U(1) quantum spin liquid is realized in the XXZ quantum spin ice (with global U(1)xZ_2 symmetry) in the perturbative regime and more recently Savary and Balents have introduced a quantum rotor model with bosonic spinons coupled to U(1) gauge fields to describe non-peturbatively the deconfined phase predicted. They studied an anisotropic quantum spin ice (QSI) model which corresponds to the XXZ QSI with an additional anisotropic coupling. They solved the quantum rotor model using a mean-field approximation combined with a large-N approximation and predicted the possibility of a U(1) liquid in addition to an exotic ferromagnetic phase. Further work by Lee et al. has addressed the more complicated fully frustrated XXZ quantum spin ice regime, where all components of the model are frustrated, by using some insights provided by the previous perturbative results. \n \nIn this thesis, we will address the non-perturbative regime of the fully frustrated XXZ QSI beyond the simplest perturbative treatment. We will begin by mapping the quantum spin ice model to a compact U(1) gauge theory with deconfined electric and magnetic monopoles. Neglecting the interaction between the gapless photon excitation and the electric charges, we will study the matter sector with only electric charges, the so-called spinons. Building up on insights provided by high order degenerate perturbation theory calculations, we will construct some symmetric spin liquid ansatz for the static part of the gauge fields. The two novel spin liquids that we construct break time reversal symmetry and thus have a non-trivial chirality. In order to solve the matter sector of the theory and determine the stability of the deconfined phases, we will introduce a novel representation of a XY quantum rotor in terms of ``exclusive" bosons, a representation which is dynamically implemented in the dilute limit. We will benchmark this mapping in different ways by comparing our results with Quantum Monte Carlo simulations and exact diagonalization in some limiting cases. Using this mapping we will compute the region of stability of the U(1) liquid phase of XXZ QSI. Within this mapping we will reproduce qualitatively the results of previous work by finding only the so-called zero and \\pi-flux U(1) liquids in the vicinity of the classical spin ice point, while improving greatly on the estimation of the exchange coupling at which the bosonic spinons condense to form a superfluid phase. In the fully frustrated XXZ QSI, we will provide evidence, using exact diagonalization of the quantum rotor model, that one of the chiral spin liquid may be realized in the strongly correlated and frustrated QSI regime, where all previous approximations break down.
We develop a self-contained theoretical framework that classifies the topological phases and critical phenomena of classical pyrochlore magnets with arbitrary spin S , subject to competing exchange and single-ion anisotropies. We work first in the monopole-free (ice-rule) limit. In the small- w regime, where the single-ion term favors low spin amplitudes, dualities reveal a dichotomy: Integer spins exhibit a continuous 3D X Y deconfinement transition, whereas half-integer spins remain in a U(1) Coulomb liquid without any transition. In the large- w regime, where the local spin amplitudes are maximized ( | S z | = S ), the macroscopic flux is quantized to multiples of 2 S . By mapping the defect structure to topological loop gases, we prove that the compatibility between the physical ice rule and the modular Z 2 S flux conservation holds at the vertex level if and only if S ≤ 3 / 2 . For S = 3 / 2 , this maps the system to the three-state Potts model, whose symmetry-allowed cubic invariant drives a first-order transition. For S ≥ 2 , no mapping to a discrete clock model exists. Using a decomposition of the partition function, we show that the only processes sensitive to the discrete Z 2 S structure carry exponentially small statistical weight and correspond to irrelevant operators at the 3D X Y fixed point, so the deconfinement transition is of the 3D X Y type. Finally, incorporating thermal monopoles, we show that they act as a symmetry-breaking effective magnetic field that severs defect strings. Consequently, the continuous transitions are rounded into crossovers, whereas the first-order S = 3 / 2 transition is predicted to survive at finite temperatures, terminating at a critical end point. Classical Monte Carlo simulations for S up to 7 / 2 corroborate the predicted crossover behavior at the accessible temperatures; these temperatures lie above the estimated critical end point, so the predicted survival of the S = 3 / 2 first-order transition remains to be tested directly.