Gauge theories are powerful theoretical physics tools that allow complex phenomena to be reduced to simple principles and are used in both high-energy and condensed matter physics. In the latter context, gauge theories are becoming increasingly popular for capturing the intricate spin correlations in spin liquids, exotic states of matter in which the dynamics of quantum spins never ceases, even at absolute zero temperature. We consider a spin system on a three-dimensional pyrochlore lattice where emergent gauge fields not only describe the spin liquid behavior at zero temperature but crucially determine the system's temperature evolution, with distinct gauge fields giving rise to different spin liquid phases in separate temperature regimes. Focusing first on classical spins, in an intermediate temperature regime, the system shows an unusual coexistence of emergent vector and tensor gauge fields where the former is known from classical spin ice systems while the latter has been associated with fractonic quasiparticles, a peculiar type of excitation with restricted mobility. Upon cooling, the system transitions into a low-temperature phase where an entropic selection mechanism depopulates the degrees of freedom associated with the tensor gauge field, rendering the system spin-ice-like. We further provide numerical evidence that in the corresponding quantum model, a spin liquid with coexisting vector and tensor gauge fields has a finite window of stability in the parameter space of spin interactions down to zero temperature. Finally, we discuss the relevance of our findings for non-Kramers magnetic pyrochlore materials.

We use strong coupling expansions to calculate the entropy function $S(T,h)$, the magnetization $M(T,h)$, and the double occupancy factor $D(T,h)$ for the half-filled triangular lattice Hubbard model as a function of temperature $T$ and Zeeman field $h$, for various values of the Hubbard parameter ratio $U/t$. These calculations converge well for temperatures larger than the exchange parameter $J=\frac{4t^2}{U}$ for moderate to large $U/t$ values. Setting $\mu=U/2$ suffices to obtain the density of half filling within a fraction of one percent at all temperatures studied for $U/t \geq 8$. We discuss the systematic variation of properties with $U/t$. The temperature dependence of entropy and the double occupancy parameter shows a mapping to an antiferromagnetic Mott insulating behavior at temperatures well above $T=J$ for $U/t\ge 10$. Convergence of the series is weaker at intermediate fields implying non-monotonic variation of spin-correlations with the Zeeman field. We discuss the relevance of the Hubbard model results to the triangular-lattice antiferromagnetic materials Lu$_3$Cu$_2$Sb$_3$O$_{14} $ (LCSO) studied recently by Yang et al [Yang et al arXiv:2102.09271 (2022)].

We investigate the ground state and critical temperature phase diagrams of the classical and quantum $S=1/2$ pyrochlore lattice with nearest-neighbor Heisenberg and Dzyaloshinskii-Moriya interactions (DMI). We consider ferromagnetic and antiferromagnetic Heisenberg exchange as well as direct and indirect DMI. Classically, three ground states are found: all-in/all-out, ferromagnetic and a locally ordered $XY$ phase, known as $\Gamma_5$, which displays an accidental classical U(1) degeneracy. Quantum zero-point energy fluctuations are found to lift the classical ground state degeneracy and select the $\psi_3$ state in most parts of the $\Gamma_5$ regime. Likewise, thermal fluctuations treated classically, select the $\psi_3$ state at $T=0^+$. In contrast, classical Monte Carlo finds that the system orders at $T_c$ in the $\psi_2$ state of $\Gamma_5$ for antiferromagnetic Heisenberg exchange and indirect DMI with a transition from $\psi_2$ to $\psi_3$ at a temperature $T_{\Gamma_5}

We investigate the ground state and critical temperature (Tc) phase diagrams of the classical and quantum S = 12 pyrochlore lattice with nearest-neighbor Heisenberg and Dzyaloshinskii-Moriya interactions (DMI). We consider ferromagnetic and antiferromagnetic Heisenberg exchange interaction as well as direct and indirect DMI. At the classical level, three ground states are found: all-in/all-out, ferromagnetic, and a locally ordered XY phase, known as ⠂5, which displays an accidental classical U(1) degeneracy at the mean-field level. Quantum zero-point energy fluctuations computed to order 1/S are found to lift the classical ground-state degeneracy and select the so-called & psi;3 state out of the degenerate manifold in most parts of the ⠂5 regime. Likewise, thermal fluctuations treated classically at the Gaussian level entropically select the & psi;3 state at T = 0+. In contrast to this low-temperature state-selection behavior, classical Monte Carlo simulations find that the system orders at Tc in the noncoplanar & psi;2 state of ⠂5 for antiferromagnetic Heisenberg exchange and indirect DMI with a transition from & psi;2 to & psi;3 at a temperature T ⠂5 < Tc. The same method finds that the system orders via a single transition at Tc directly into the & psi;3 state for most of the region with ferromagnetic Heisenberg exchange and indirect DMI. Such ordering behavior at Tc for the S = 12 quantum model is corroborated by high-temperature series expansion. To investigate the T = 0 quantum ground state of the model, we apply the pseudo-fermion functional renormalization group (PFFRG). The quantum paramagnetic phase of the pure antiferromagnetic S = 12 Heisenberg model is found to persist over a finite region in the phase diagram for both direct or indirect DMI. Interestingly, we find that a combined ferromagnetic Heisenberg and indirect DMI, near the boundary of ferromagnetism and ⠂5 antiferromagnetism, may potentially realize a T = 0 quantum ground state lacking conventional magnetic order. Otherwise, for the largest portion of the phase diagram, PFFRG finds the same long-range ordered phases (all-in/all-out, ferromagnetic, and ⠂5) as in the classical model.

We study the ordered phases of the S = 1/2 fcc Heisenberg antiferromagnet, with first- and second-neighbor interactions, using perturbative series expansions at zero temperature. From calculations of ground-state energies we determine the regions of stability of semiclassical AF1, AF2, and AF3 phases. For the pure nearest-neighbor case our results suggest that AF1 is favored over AF3, a result in disagreement with linear spin-wave theory, but in agreement with other more recent work. We also investigate the two possible AF2 phases and locate the crossover between AF3 and AF2 at J2/J1 & SIM; 0.535.

We develop finite temperature strong coupling expansions for the SU(N) Hubbard Model in powers of $\beta t$, $w=\exp{(-\beta U)}$ and ${1\over \beta U}$ for arbitrary filling. The expansions are done in the grand canonical ensemble and are most useful at a density of one particle per site, where for $U$ larger than or of order the Bandwidth, the expansions converge over a wide temperature range $t^2/U \ \lesssim \ T \ \lesssim \ 10 U$. By taking the limit $w\to 0$, valid at temperatures much less than $U$, the expansions turn into a high temperature expansion for a dressed SU(N) Heisenberg model that includes nearest-neighbor exchange, further neighbor exchanges and ring exchanges known from the $T=0$ perturbation theory of the SU(2) Hubbard model. Below a filling of one particle per site, the $w\to 0$ limit corresponds to an effective $t-J$ model. The onset of strong correlations can be identified by a plateau-like behavior in the entropy as a function of temperature. At small deviations from one particle per site, the expansions can be arranged in powers of a small parameter $\delta=1-n$, the deviation from one particle per site, where the leading $\beta t$ dependent terms correspond to holes sloshing around in a disordered SU(N) background. We use these expansions to calculate the thermodynamic properties of the model at moderate and high temperatures over a wide parameter range.

We investigate the ground state and critical temperature phase diagrams of the classical and quantum S=1/2 pyrochlore lattice with nearest-neighbor Heisenberg and Dzyaloshinskii-Moriya interactions (DMI). We consider ferromagnetic and antiferromagnetic Heisenberg exchange as well as direct and indirect DMI. Classically, three ground states are found: all-in/all-out, ferromagnetic and a locally ordered XY phase, known as Γ_5, which displays an accidental classical U(1) degeneracy. Quantum zero-point energy fluctuations are found to lift the classical ground state degeneracy and select the ψ_3 state in most parts of the Γ_5 regime. Likewise, thermal fluctuations treated classically, select the ψ_3 state at T=0^+. In contrast, classical Monte Carlo finds that the system orders at T_c in the ψ_2 state of Γ_5 for antiferromagnetic Heisenberg exchange and indirect DMI with a transition from ψ_2 to ψ_3 at a temperature T_Γ_5 <T_c. The same method finds that the system orders via a single transition at T_c directly into the ψ_3 state for most of the region with ferromagnetic Heisenberg exchange and indirect DMI. Such ordering behavior at T_c for the S=1/2 quantum model is corroborated by high-temperature series expansion. To investigate the T=0 quantum ground states, we apply the pseudo-fermion functional renormalization group (PFFRG). The quantum paramagnetic phase of the pure antiferromagnetic S=1/2 Heisenberg model is found to persist over a finite region in the phase diagram for both direct or indirect DMI. We find that near the boundary of ferromagnetism and Γ_5 antiferromagnetism the system may potentially realize a quantum ground state lacking conventional magnetic order. Otherwise, for the largest portion of the phase diagram, PFFRG finds the same ordered phases as in the classical model.

We use finite temperature strong coupling expansions to calculate thermodynamic properties of the Honeycomb-lattice SU(4) Hubbard model. We present numerical results for various properties including chemical potential, compressibility, entropy and specific heat as a function of temperature and density at several $U/t$ values. We study the onset of charge incompressibility and Mott gaps as the temperature is lowered at integer densities. In the incompressible Mott regime, the expansions are recast into a high temperature expansion for a generalized spin model with SU(4) symmetry, which is then used to study the convergence of strong coupling expansions in t/U. We discuss lessons that can be drawn from high temperature properties of a simple Hubbard model regarding Twisted Bilayer Graphene (TBG) and other magic-angle flat-band systems.

Using finite temperature strong coupling expansions for the SU(N) Hubbard Model, we calculate the thermodynamic properties of the model in the infinite-$U$ limit for arbitrary density $0\leq \rho \leq 1$ and all $N$. We express the ferromagnetic susceptibility of the model as a Curie term plus a $\Delta \chi$, an excess susceptibility above the Curie-behavior. We show that, on a bipartite lattice, graph by graph the contributions to $\Delta \chi$ are non-negative in the limit that the hole density $\delta=1-\rho$ goes to zero. By summing the contributions from all graphs consisting of closed loops we find that the low hole-density ferromagnetic susceptibility diverges exponentially as $\exp{\Delta /T}$ as $T \to 0$ in two and higher dimensions. This demonstrates that Nagaoka-Thouless ferromagnetic state exists as a thermodynamic state of matter at low enough density of holes and sufficiently low temperatures. The constant $\Delta$ scales with the SU(N) parameter $N$ as $1/N$ implying that ferromagnetism is gradually weakened with increasing $N$ as the characteristic temperature scale for ferromagnetic order goes down.

We study the thermodynamic behavior of modified spin-S Kitaev models introduced by Baskaran, Sen, and Shankar [Phys. Rev. B 78, 115116 (2008)PRBMDO1098-012110.1103/PhysRevB.78.115116]. These models have the property that for half-odd-integer spins their eigenstates map on to those of spin-1/2 Kitaev models, with well-known highly entangled quantum spin-liquid states and Majorana fermions. For integer spins, the Hamiltonian is made out of commuting local operators. Thus, the eigenstates can be chosen to be completely unentangled between different sites, though with a significant degeneracy for each eigenstate. For half-odd-integer spins, the thermodynamic properties can be related to the spin-1/2 Kitaev models apart from an additional degeneracy. Hence we focus here on the case of integer spins. We use transfer matrix methods, high-temperature expansions, and Monte Carlo simulations to study the thermodynamic properties of ferromagnetic and antiferromagnetic models with spin S=1 and S=2. Apart from large residual entropies, which all the models have, we find that they can have a variety of different behaviors. Transfer matrix calculations show that for the different models, the correlation lengths can be finite as T→0, become critical as T→0, or diverge exponentially as T→0. The Z_{2} flux variable associated with each hexagonal plaquette saturates at the value +1 as T→0 in all models except the S=1 antiferromagnet where the mean flux remains zero as T→0. We provide qualitative explanations for these results.

We use series expansion methods to investigate the zero-temperature phase diagram of a spin-$\frac{1}{2}$ Heisenberg frustrated bilayer model. For different parameter regions the model shows two related antiferromagnetic phases as well as a nonmagnetic dimerized phase. The phase boundaries are located to high precision and agree very well with a previous calculation using different methods. The triplon spectrum in the dimerized phase is also studied.

Antiferromagnetic quantum spin systems can exhibit a transition between collinear and spiral ground states, driven by frustration. Classically this is a smooth crossover and the crossover point is termed a Lifshitz point. Quantum fluctuations change the nature of the transition. In particular it has been argued previously that in the two-dimensional (2D) case a spin liquid (SL) state is developed in the vicinity of the Lifshitz point, termed a Lifshitz SL. In the present work, using a field theory approach, we solve the Lifshitz quantum phase transition problem for the 2D frustrated XY-model. Specifically, we show that, unlike the SU(2) symmetric Lifshitz case, in the XY-model the SL exists only at the critical point. At zero temperature we calculate nonuniversal critical exponents in the Neel and in the spin spiral state and relate these to properties of the SL. We also solve the transition problem at a finite temperature and discuss the role of topological excitations.

We investigate the ground states of an Ising model with a transverse field on the square lattice, with additional frustrating second-neighbour Ising interactions, using series expansion methods. The phase boundaries are located to high precision. No strong evidence for the presence of a tricritical point is seen, but it cannot be excluded.

We use series expansion methods to investigate the phase diagram of a spin-1/2 Heisenberg antiferromagnet on the triangular lattice with first- and second-neighbor interactions. We find regions of 120 degrees and collinear "stripe" order, separated by an intermediate nonmagnetic phase, in agreement with results obtained previously using other methods. Magnon excitation spectra in the ordered phases are also obtained, and discussed.

We use series expansion methods to investigate the phase diagram of a spin-1/2 Heisenberg antiferromagnet on a diamond lattice with first- and second-neighbor interactions. Using series expansions at T = 0, we find an apparent second-order transition from collinear Neel order to an incommensurate spiral with wave vector (k, k, 0) at J(2)/J(1) similar to 0.18, considerably higher than the classical value 1/8. We extend the calculation to the case of tetragonal distortion, as occurs in the material CuRh2O4. Here we find a clear second-order transition from Neel order to a (0, 0, k) spiral.

represents a band of conduction electrons, interacting via a spin-exchange term with a set of immobile s = 1 2 spins Si (f electrons). The model has been extensively studied in connection with a class of materials known as “Kondo insulators” (J > 0), and in connection with the manganites (J < 0). Despite the apparent simplicity of the model, in which neither the conduction electrons nor localized spins interact directly among themselves, the spin exchange leads to a strongly-correlated many-body system. No exact results are known for either ground state or thermodynamic properties for general J/t, in any dimension. The model incorporates two competing physical processes. In the strong-coupling (large |J |) limit, the conduction electrons are “frozen out” via the formation of local singlets (J > 0) or triplets (J < 0). In either case there will be a gap to spin excitations and spin correlations will be short ranged. On the other hand, at weak coupling, the conduction electrons can induce the usual RKKY interaction between localized spins, giving rise to possible magnetically ordered phases with no spin gap and long-range correlations. In one dimension there will be a smooth crossover from large |J | to small |J | behaviour, but in higher dimension a quantum phase transition is expected. A great deal of work has been carried out on the one dimensional model, using a variety of analytic and numerical methods, and we refer the reader to a recent review. In higher dimension there have been mean-field approaches, quantum Monte Carlo calculations, and a series expansion study. These studies, which are all for the half-filled case, conclude that a quantum phase transition, at which the spin gap vanishes continuously, occurs at (J/t)c ≃ 1.45± 0.05 in the 2D J > 0 case, while Refs. 6,8 give (J/t)c ≃ 1.833, 2.0 respectively for the 3D J > 0 case. There have not been, to our knowledge, any similar studies for the case of ferromagnetic coupling. Our aim in this paper is to study the Kondo lattice model in 1, 2 and 3-dimensions via series expansion methods. We have considerably extended the calculations of Ref. 8, by obtaining longer series, by using also expansions about the Ising limit, and by studying also the energies of elementary excitations. Linked-cluster series expansions have been used successfully for many years to study strongly interacting lattice models. A recent review describes the basic approach and some of the results which have been obtained. The method is applicable in any dimension, is particularly suited to locating critical points and is free from finite size corrections or minus sign problems which hamper other numerical approaches. On the other hand good convergence may be limited to particular regions of the phase diagram. The Hamiltonian is written in the generic form H = H0 + λV where H0 has a simple known ground state. The remaining term(s) in H are treated perturbatively, to high order. In this way the ground state energy, correlations, susceptibilities, etc, are expressed as power series in λ. These are then analysed by standard methods. An extension of the basic linked-cluster method allows the computation of the full dispersion relation for elementary excitations, which can yield energy gaps. For the present model the simplest choice is to take H0 = J ∑

Three decades ago, Ioffe and Larkin pointed out a generic mechanism for the formation of a gapped spin liquid. In the case when a classical two-dimensional (2D) frustrated Heisenberg magnet undergoes a Lifshitz transition between a collinear Ned phase and a spin-spiral phase, quantum effects usually lead to the development of a spin-liquid phase sandwiched between the Ned and spin-spiral phases. In this work, using field theory techniques, we study properties of this universal spin-liquid phase. We examine the phase diagram near the Lifshitz point and calculate the positions of critical points, excitation spectra, and spin-spin correlation functions. We argue that the spin liquid in the vicinity of 2D Lifshitz point (LP) is similar to the gapped Haldane phase in integer-spin one-dimensional chains. We also consider a specific example of a frustrated system with the spiral-Ned LP, the J(1)-J(3) antiferromagnet on the square lattice that manifests the spin-liquid behavior. We present numerical series expansion calculations for this model and compare results of the calculations with predictions of the developed field theory.

Quantum spin ice materials, pyrochlore magnets with competing Ising and transverse exchange interactions, have been widely discussed as candidates for a quantum spin-liquid ground state. Here, motivated by quantum chemical calculations for Pr pyrochlores, we present the results of a study for frustrated transverse exchange. Using a combination of variational calculations, exact diagonalization, numerical linked-cluster and series expansions, we find that the previously studied U(1) quantum spin liquid, in its π-flux phase, transforms into a nematic quantum spin liquid at a high-symmetry, SU(2) point.