Finite-temperature Phase Diagram Research Articles

Charge-order on the triangular lattice: Effects of next-nearest-neighbor attraction in finite temperatures

The extended Hubbard model in the atomic limit, which is equivalent to lattice S=1/2 fermionic gas, is considered on the triangular lattice. The model includes onsite Hubbard U interaction and both nearest-neighbor (W1) and next-nearest-neighbor (W2) density–density intersite interactions. The variational approach treating the U term exactly and the Wl terms in the mean-field approximation is used to investigate thermodynamics of the model and to find its finite temperature (T>0) phase diagrams (as a function of particle concentration) for W1>0 and W2<0. Two different types of charge-order (i.e., DCO and TCO phases) within 3×3 unit cells as well as the nonordered (NO) phase occur on the diagram. Moreover, several kinds of phase-separated (PS) states (NO/DCO, DCO/DCO, DCO/TCO, and TCO/TCO) are found to be stable for fixed concentration. Attractive W2<0 stabilizes PS states at T=0 and it extends the regions of their occurrence at T>0. The evolution of the diagrams with increasing of |W2|/W1 is investigated. It is found that some of the PS states are stable only at T>0. Two different critical values of |W2|/W1 are determined for the PS states, in which two ordered phases of the same type (i.e., two domains of the DCO or TCO phase) coexist.

Continuous-Variable Assisted Thermal Quantum Simulation.

Simulation of a quantum many-body system at finite temperatures is crucially important but quite challenging. Here we present an experimentally feasible quantum algorithm assisted with continuous variable for simulating quantum systems at finite temperatures. Our algorithm has a time complexity scaling polynomially with the inverse temperature and the desired accuracy. We demonstrate the quantum algorithm by simulating a finite temperature phase diagram of the quantum Ising and Kitaev models. It is found that the important crossover phase diagram of the Kitaev ring can be accurately simulated by a quantum computer with only a few qubits and thus the algorithm may be implementable on current quantum processors. We further propose a protocol with superconducting or trapped ion quantum computers.

Phase diagrams and hysteresis behavior of the mixed spin-7/2 and spin-1/2 Ising model

The mixed spin-7/2 and spin-1/2 Ising model with a crystal field in the absence and presence of an external longitudinal magnetic field is investigated within the framework both of the renormalization group (RG) method and Monte Carlo simulation (MCS). First, we have determined the ground-state phase diagram. Then, using RG technique, the finite temperature phase diagrams of this model are plotted for the two- and three-dimensional cases by following the flow in the parameters space of the Hamiltonian and evaluating the free energy and its isotherm derivative at low temperatures. Our results show that the model exhibits first- and second-order phase transitions as well as critical end-points. In addition, by linearizing the RG transformation at the vicinity of the fixed points of the second-order transition, we have determined the critical exponents. The MCS is also employed to validate the results obtained previously by renormalization, and to examine the influence of an external magnetic field on the magnetic properties and hysteresis loops of the system.

Charge-Order on the Triangular Lattice: A Mean-Field Study for the Lattice S = 1/2 Fermionic Gas.

The adsorbed atoms exhibit tendency to occupy a triangular lattice formed by periodic potential of the underlying crystal surface. Such a lattice is formed by, e.g., a single layer of graphane or the graphite surfaces as well as (111) surface of face-cubic center crystals. In the present work, an extension of the lattice gas model to fermionic particles on the two-dimensional triangular (hexagonal) lattice is analyzed. In such a model, each lattice site can be occupied not by only one particle, but by two particles, which interact with each other by onsite U and intersite and (nearest and next-nearest-neighbor, respectively) density-density interaction. The investigated hamiltonian has a form of the extended Hubbard model in the atomic limit (i.e., the zero-bandwidth limit). In the analysis of the phase diagrams and thermodynamic properties of this model with repulsive , the variational approach is used, which treats the onsite interaction term exactly and the intersite interactions within the mean-field approximation. The ground state () diagram for as well as finite temperature () phase diagrams for are presented. Two different types of charge order within unit cell can occur. At , for phase separated states are degenerated with homogeneous phases (but removes this degeneration), whereas attractive stabilizes phase separation at incommensurate fillings. For and only the phase with two different concentrations occurs (together with two different phase separated states occurring), whereas for small repulsive the other ordered phase also appears (with tree different concentrations in sublattices). The qualitative differences with the model considered on hypercubic lattices are also discussed.

Dimensional crossover in ultracold Fermi gases from functional renormalization

We investigate the dimensional crossover from three to two dimensions in an ultracold Fermi gas across the whole BCS-BEC crossover. Of particular interest is the strongly interacting regime as strong correlations are more pronounced in reduced dimensions. Our results are obtained from first principles within the framework of the functional renormalisation group (FRG). Here, the confinement of the transverse direction is imposed by means of periodic boundary conditions. We calculate the equation of state, the gap parameter at zero temperature and the superfluid transition temperature across a wide range of transversal confinement length scales. Particular emphasis is put on the determination of the finite temperature phase diagram for different confinement length scales. In the end, our results are compared with recent experimental observations and we discuss them in the context of other theoretical works.

Onsager reaction field theory applied to the phase diagram of Heisenberg chain with ferromagnetic long-range interaction and antiferromagnetic nearest-neighbor interaction

Onsager reaction field theory is used to investigate the one-dimensional ferromagnetic long-range interacting spin chain with the antiferromagnetic nearest-neighbor interaction (NNI) [Formula: see text]. The ferromagnetic long-range interactions considered in this paper decay as [Formula: see text] with the distance [Formula: see text] between lattice sites. It is found that both the zero temperature and finite-temperature phase diagrams of the system are strongly affected by the interplay between ferromagnetic long-range and antiferromagnetic NNIs. The critical temperature and the uniform susceptibility are obtained as a function of [Formula: see text] and [Formula: see text]. At finite temperatures and in the region [Formula: see text] in which [Formula: see text] is dependent of [Formula: see text], the ferromagnetic-paramagnetic phase transition survives for [Formula: see text] and no phase transition exists for [Formula: see text]. At [Formula: see text], the ferromagnetic-antiferromagnetic phase transition happens at zero temperature for [Formula: see text]. The ground state of the system keeps ferromagnetic when [Formula: see text]. But for [Formula: see text], the system becomes antiferromagnetic at all temperatures.

The view of TK-SVM on the phase hierarchy in the classical kagome Heisenberg antiferromagnet

We illustrate how the tensorial kernel support vector machine (TK-SVM) can probe the hidden multipolar orders and emergent local constraint in the classical kagome Heisenberg antiferromagnet. We show that TK-SVM learns the finite-temperature phase diagram in an unsupervised way. Moreover, in virtue of its strong interpretability, it identifies the tensorial quadrupolar and octupolar orders, which define a biaxial D 3h spin nematic, and the local constraint that underlies the selection of coplanar states. We then discuss the disorder hierarchy of the phases, which can be inferred from both the analytical order parameters and an SVM bias parameter. For completeness we mention that the machine also picks up the leading correlations in the dipolar channel at very low temperature, which are however weak compared to the quadrupolar and octupolar orders. Our work shows how TK-SVM can facilitate and speed up the analysis of classical frustrated magnets.

Ultradilute self-bound quantum droplets in Bose–Bose mixtures at finite temperature* *Project supported by the Australian Research Council’s (ARC) Discovery Program (Grant Nos. DE180100592 and DP190100815), (Grant No. DP180102018), and (Grant No. DP170104008).

We theoretically investigate the finite-temperature structure and collective excitations of a self-bound ultradilute Bose droplet in a flat space realized in a binary Bose mixture with attractive inter-species interactions on the verge of mean-field collapse. As the droplet formation relies critically on the repulsive force provided by Lee–Huang–Yang quantum fluctuations, which can be easily compensated by thermal fluctuations, we find a significant temperature effect in the density distribution and collective excitation spectrum of the Bose droplet. A finite-temperature phase diagram as a function of the number of particles is determined. We show that the critical number of particles at the droplet-to-gas transition increases dramatically with increasing temperature. Towards the bulk threshold temperature for thermally destabilizing an infinitely large droplet, we find that the excitation-forbidden, self-evaporation region in the excitation spectrum, predicted earlier by Petrov using a zero-temperature theory, shrinks and eventually disappears. All the collective excitations, including both surface modes and compressional bulk modes, become softened at the droplet-to-gas transition. The predicted temperature effects of a self-bound Bose droplet in this work could be difficult to measure experimentally due to the lack of efficient thermometry at low temperatures. However, these effects may already present in the current cold-atom experiments.

Finite temperature auxiliary field quantum Monte Carlo in the canonical ensemble.

Finite temperature auxiliary field-based quantum Monte Carlo methods, including determinant quantum Monte Carlo and Auxiliary Field Quantum Monte Carlo (AFQMC), have historically assumed pivotal roles in the investigation of the finite temperature phase diagrams of a wide variety of multidimensional lattice models and materials. Despite their utility, however, these techniques are typically formulated in the grand canonical ensemble, which makes them difficult to apply to condensates such as superfluids and difficult to benchmark against alternative methods that are formulated in the canonical ensemble. Working in the grand canonical ensemble is furthermore accompanied by the increased overhead associated with having to determine the chemical potentials that produce desired fillings. Given this backdrop, in this work, we present a new recursive approach for performing AFQMC simulations in the canonical ensemble that does not require knowledge of chemical potentials. To derive this approach, we exploit the convenient fact that AFQMC solves the many-body problem by decoupling many-body propagators into integrals over one-body problems to which non-interacting theories can be applied. We benchmark the accuracy of our technique on illustrative Bose and Fermi-Hubbard models and demonstrate that it can converge more quickly to the ground state than grand canonical AFQMC simulations. We believe that our novel use of HS-transformed operators to implement algorithms originally derived for non-interacting systems will motivate the development of a variety of other methods and anticipate that our technique will enable direct performance comparisons against other many-body approaches formulated in the canonical ensemble.

Phases and collective modes of bosons in a triangular lattice at finite temperature: A cluster mean field study

Motivated by the realization of Bose-Einstein condensates (BEC) in non-cubic lattices, in this work we study the phases and collective excitation of bosons with nearest neighbor interaction in a triangular lattice at finite temperature, using mean field (MF) and cluster mean field (CMF) theory. We compute the finite temperature phase diagram both for hardcore and softcore bosons, as well analyze the effect of correlation arising due to lattice frustration and interaction systematically using CMF method. A semi-analytic estimate of the transition temperatures between different phases are derived within the framework of MF Landau theory, particularly for hardcore bosons. Apart from the usual phases such as density waves (DW) and superfluid (SF), we also characterize different supersolids (SS). These phases and their transitions at finite temperature are identified from the collective modes. The low lying excitations, particularly Goldstone and Higgs modes of the supersolid can be detected in the ongoing cold atom experiments.

Mixed temperature-dependent order parameters in the extended Hubbard model

The extended Hubbard model can host s-wave, d-wave and p-wave superconducting phases depending on the values of the on-site and nearest-neighbour interactions. Upon detailed examination of the free energy functional of the gap in this model, we show that these symmetries are often dependent on temperature. The critical points of this functional are constrained by symmetry and allow us to formulate stringent conditions on the temperature profile of the gap function, applicable to other models as well. We discuss the finite temperature phase diagram of the extended Hubbard model, and point out the existence of symmetry transitions below T c. Understanding the nature of these transitions is crucial to assessing the symmetry of unconventional superconductors.

A computational examination of the zeta and eta phases in the hafnium nitrides

AbstractThe hafnium‐rich portion of the of the hafnium‐nitrogen phase diagram is dominated by a substoichiometric rocksalt HfN1‐x, the ζ‐Hf4N3−x, the η‐Hf3N2−x, and the elemental Hf phase. The zeta and eta nitride phases have a close packed metal atom stacking sequence but their nitrogen atom ordering has yet to be concretely identified. With respect to the composition of these phases, recent computational studies of their phase stability using density functional theory (DFT) are not in agreement with reported experimental observations. In this work, we re‐examine the phase stability of the zeta and eta phases using DFT combined with enumerated searches using the known metal atom stacking sequences of these phases but with variable carbon concentration and ordering. We have found new structures for the zeta and eta phases that are now in better agreement with experimental findings. Furthermore, we report a new eta phase, ‐Hf12N7, which lies on the convex hull and has a nitrogen atom ordering that is substantially different from the zeta phase. This work also demonstrates the importance of configurational entropy in dictating the finite temperature phase diagrams in this system.

Ground States Phase Diagrams and Magnetizations Properties of Ferrimagnetic Model on Decorated Hexagonal Nanolattice: Monte Carlo Study

The ground states phase diagrams and magnetizations properties of ferrimagnetic model on decorated hexagonal nanolattice have been studied via Monte Carlo simulations. The shape of the phase diagrams depends of the values of the magnetic parameters given in the Hamiltonian. The phase diagrams show some key features: coexistence between regions, points where two, three, four and five and states can coexist. This richness of the ground state phase diagrams can serve as a guide for exploring interesting regions of the model’s finite temperature phase diagrams. The transition temperatures have been deduced for different values of exchange interactions between the atoms of spins moments(S). The effect of crystal field and exchange interactions on magnetization has been investigated. The magnetic coercive field and remanent magnetization are obtained for different parameters such as: exchange couplings and temperatures values. The superparamagnetic behavior has been found at the transition temperature.

Supersolid phase of the extended Bose-Hubbard model with an artificial gauge field

We examine the zero and finite temperature phase diagrams of soft-core bosons of the extended Bose-Hubbard model on a square optical lattice. To study various quantum phases and their transitions we employ single-site and cluster Gutzwiller mean-field theory. We have observed that the Mott insulator phase vanishes above a critical value of nearest-neighbour interaction and the supersolid phase occupies a larger region in the phase diagram. We show that the presence of artificial gauge field enlarges the domain of supersolid phase. The finite temperature destroys the crystalline structure of the supersolid phase and thereby favours normal fluid to superfluid phase transition. The presence of an envelope harmonic potential demonstrates coexistence of different phases and at $z~k_{B}T\geqslant V$, thermal energy comparable and higher to the long-range interaction energy, the supersolidity of the system is destroyed.

Helical spin liquid in a triangular XXZ magnet from Chern-Simons theory

We propose a finite-temperature phase diagram for the 2D spin-$1/2$ $J_1-J_2$ $XXZ$ antiferromagnet on the triangular lattice. Our analysis, based on a composite fermion representation, yields several phases. This includes a zero-temperature helical spin liquid with $N=6$ {\it anisotropic} Dirac cones, and with nonzero vector chirality implying a broken $\mathbb{Z}_2$ symmetry. It is terminated at $T=0$ by a continuous quantum phase transition to $120^\circ$ ordered state around $J_2/J_1\approx0.089$ in the XX limit; these phases share a double degeneracy, which persists to finite $T$ above the helical spin liquid. By contrast, at $J_2/J_1 \simeq 0.116$, the transition into a stripe phase appears as first order. We further discuss experimental and numerical consequences of the helical order and the anisotropic nature of the Dirac dispersion.

Charting the scaling region of the Ising universality class in two and three dimensions

We study the behaviour of a universal combination of susceptibility and correlation length in the Ising model in two and three dimensions, in presence of both magnetic and thermal perturbations, in the neighbourhood of the critical point. In three dimensions we address the problem using a parametric representation of the equation of state. In two dimensions we make use of the exact integrability of the model along the thermal and the magnetic axes. Our results can be used as a sort of "reference frame" to chart the critical region of the model. While our results can be applied in principle to any possible realization of the Ising universality class, we address in particular, as specific examples, three instances of Ising behaviour in finite temperature QCD related in various ways to the deconfinement transition. In particular, in the last of these examples, we study the critical ending point in the finite density, finite temperature phase diagram of QCD. In this finite density framework, due to well know sign problem, Montecarlo simulations are not possible and thus a direct comparison of experimental results with QFT/Statmech predictions like the one we discuss in this paper may be important. Moreover in this example it is particularly difficult to disentangle "magnetic-like" from "thermal-like" observables and thus universal quantities which do not need a precise identification of the magnetic and thermal axes, like the one we address in this paper, can be particularly useful.

Nonlocal exchange interactions in strongly correlated electron systems

We study the influence of ferromagnetic nonlocal exchange on correlated electrons in terms of a $SU(2)$-Hubbard-Heisenberg model and address the interplay of on-site interaction induced local moment formation and the competition of ferromagnetic direct and antiferromagnetic kinetic exchange interactions. In order to simulate thermodynamic properties of the system in a way that largely accounts for the on-site interaction driven correlations in the system, we advance the correlated variational scheme introduced in [M. Sch\"uler et al., Phys. Rev. Lett. 111, 036601 (2013)] to account for explicitily symmetry broken electronic phases by introducing an auxiliary magnetic field. After benchmarking the method against exact solutions of a finite system, we study the $SU(2)$-Hubbard-Heisenberg model on a square lattice. We obtain the $U$-$J$ finite temperature phase diagram of a $SU(2)$-Hubbard-Heisenberg model within the correlated variational approach and compare to static mean field theory. While the generalized variational principle and static mean field theory yield transitions from dominant ferromagnetic to antiferromagnetic correlations in similar regions of the phase diagram, we find that the nature of the associated phase tranistions differs between the two approaches. The fluctuations accounted for in the generalized variational approach render the transitions continuous, while static mean field theory predicts discontinuous transitions between ferro- and antiferromagnetically ordered states.

Quantum critical thermal transport in the unitary Fermi gas

Strongly correlated systems are often associated with an underlying quantum critical point which governs their behavior in the finite temperature phase diagram. Their thermodynamical and transport properties arise from critical fluctuations and follow universal scaling laws. Here, we develop a microscopic theory of thermal transport in the quantum critical regime expressed in terms of a thermal sum rule and an effective scattering time. We explicitly compute the characteristic scaling functions in a quantum critical model system, the unitary Fermi gas. Moreover, we derive an exact thermal sum rule for heat and energy currents and evaluate it numerically using the nonperturbative Luttinger-Ward approach. For the thermal scattering times we find a simple quantum critical scaling form. Together, the sum rule and the scattering time determine the heat conductivity, thermal diffusivity, Prandtl number and sound diffusivity from high temperatures down into the quantum critical regime. The results provide a quantitative description of recent sound attenuation measurements in ultracold Fermi gases.

Unveiling the Finite Temperature Physics of Hydrogen Chains via Auxiliary Field Quantum Monte Carlo.

The ability to accurately predict the finite temperature properties and phase diagrams of realistic quantum solids is central to uncovering new phases and engineering materials with novel properties ripe for device applications. Nonetheless, there remain comparatively few many-body techniques capable of elucidating the finite temperature physics of solids from first principles. In this work, we take a significant step toward developing such a technique by generalizing our previous, exact fully ab initio finite temperature Auxiliary Field Quantum Monte Carlo (FT-AFQMC) method to model periodic solids and employing it to uncover the finite temperature physics of periodic hydrogen chains. Our chains' unit cells consist of 10 hydrogen atoms modeled in a minimal basis, and we sample 5 k-points from the first Brillouin zone to arrive at a supercell consisting of 50 orbitals and 50 electrons. Based upon our calculations of these chains' many-body energies, free energies, entropies, heat capacities, double and natural occupancies, and charge and spin correlation functions, we outline their metal-insulator and magnetic ordering as a function of both H-H bond distance and temperature. At low temperatures approaching the ground state, we observe both metal-insulator and ferromagnetic-antiferromagnetic crossovers at bond lengths between 0.5 and 0.75 Å. We then demonstrate how this low-temperature ordering evolves into a metallic phase with decreasing magnetic order at higher temperatures. In order to contextualize our results, we compare the features we observe to those previously seen in one-dimensional, half-filled Hubbard models at finite temperature and in ground state hydrogen chains. Interestingly, we identify signatures of the Pomeranchuk effect in hydrogen chains for the first time and show that spin and charge excitations that typically arise at distinct temperatures in the Hubbard model are indistinguishably coupled in these systems. Beyond qualitatively revealing the many-body phase behavior of hydrogen chains in a numerically exact manner without invoking the phaseless approximation, our efforts shed light on the further theoretical developments that will be required to construct the phase diagrams of the more complex transition metal, lanthanide, and actinide solids of longstanding interest to physicists.

A novel critical behavior of the spin-1 Blume–Capel model with a distance-dependent nearest-neighbor exchange interaction and magneto-elastic coupling

A generalized spin-1 Blume–Capel model with distance/volume dependent nearest-neighbor exchange interaction is introduced and investigated using the standard methods of statistical mechanics. Besides of the volume-dependent magnetic energy, the static electromagnetic energy and anharmonic Einstein phonon contribution are also taken into account. Taking the simple volume dependence of all energy contributions we have obtained the equation of state, magnetic moment, internal and Helmholtz free energy of the system. The ground-state and finite-temperature phase diagrams are obtained and discussed in detail. Is it shown that the generalized spin-1 Blume–Capel model exhibits a novel critical behavior appearing due to magnetostriction and thermal volume variations. The presented approach is very universal and easily applicable to many other theoretical models in different fields of solid state physics.