Finite-temperature Phase Diagram Research Articles

Phase transitions of geometrically frustrated mixed spin-1/2 and spin-1 Ising-Heisenberg model on diamond-like decorated planar lattices

Phase transitions of the mixed spin-1/2 and spin-1 Ising-Heisenberg model on several decorated planar lattices consisting of interconnected diamonds are investigated within the framework of the generalized decoration-iteration transformation. The main attention is paid to the systematic study of the finite-temperature phase diagrams in dependence on the lattice topology. The critical behaviour of the hybrid quantum-classical Ising-Heisenberg model is compared with the relevant behaviour of its semi-classical Ising analogue. It is shown that both models on diamond-like decorated planar lattices exhibit a striking critical behaviour including reentrant phase transitions. The higher the lattice coordination number is, the more pronounced reentrance may be detected.

U(1) slave-particle study of the finite-temperature doped Hubbard model in one and two dimensions

One-dimensional systems have unusual properties such as fractionalization of degrees of freedom. The occurrence of similar phenomena in higher dimensional systems has been considered in the literature for the description of quantum spin liquids and some non-fermi liquid phases. In this work we construct a mean field (MF) theory of the Hubbard model which is based on a representation of the electronic fields that explicitly introduces a separation of the charge and spin degrees of freedom (the so-called Zou–Anderson transformation) and study the finite-temperature phase diagram for the Hubbard chain and square lattice. The mean field variables are defined along the links of the underlying lattice. We obtain the spectral function and identify the regions of higher spectral weight with the fractionalized fermionic (spin) and bosonic (charge) excitations.

Temperature-Driven Structural Phase Transition for Trapped Ions and a Proposal for its Experimental Detection

A Wigner crystal formed with trapped ions can undergo a structural phase transition, which is determined only by the mechanical conditions on a classical level. Instead of this classical result, we show that through consideration of quantum and thermal fluctuation, a structural phase transition can be driven solely by a change in the system's temperature. We determine a finite-temperature phase diagram for trapped ions using the renormalization group method and the path integral formalism, and propose an experimental scheme to observe the predicted temperature-driven structural phase transition, which is well within the reach of the current ion trap technology.

First-principles study of atomic ordering in bcc Cu–Al

The order–disorder transitions and phase stability in the body centered cubic structure of Cu–Al binary alloys are studied by means of theoretical methods. The total energy of different ordered compounds sharing a common bcc Bravais lattice was calculated within the framework of density functional theory. A set of effective cluster interactions was calculated through a cluster expansion (CE) of the total energies. The finite temperature phase diagram of bcc Cu–Al was obtained using the CE formalism coupled with the cluster variation method calculation of the configurational entropy. These results are confronted with a simpler semi-empirical approach based on effective pair interactions obtained from experiment. Both approaches predict a single first-order A2/DO3 transition for compositions close to Cu3Al, in agreement with the most recent experimental results.

Comment on “Direct Mapping of the Finite Temperature Phase Diagram of Strongly Correlated Quantum Models”

In their Letter, Zhou, Kato, Kawashima, and Trivedi claim that finite-temperature critical points of strongly correlated quantum models emulated by optical lattice experiments can generically be deduced from kinks in the derivative of the density profile of atoms in the trap with respect to the external potential, $\kappa = -dn(r)/dV(r)$. In this comment we demonstrate that the authors failed to achieve their goal: to show that under realistic experimental conditions critical densities $n_c(T,U)$ can be extracted from density profiles with controllable accuracy.

Thermal phase transitions of supersolids in the extended Bose-Hubbard model

We investigate numerically the finite-temperature phase diagrams of the extended Bose-Hubbard model in a two-dimensional square lattice. In particular, we focus on the melting of supersolid phases of two different crystal orderings, stripe and star orders, arising from the competition of the nearest- and next-nearest -neighbor interactions in the vicinity of quarter filling. The two crystal orders are the result of broken translational symmetry in either one or in both $x$, and $y$ directions. The broken gauge symmetry of the supersolids are found to be restored via a Kosterlitz-Thouless transition while the broken translational symmetries are restored via a single second-order phase transition, instead of two second-order transitions in the Ising universality class. On the other hand, the phase transitions between the star and stripe orders are first order in nature.

Phase diagram and deformed phase separation for a trapped Fermi gas with population imbalance and BCS pairing interaction

We study the phase separated state of an ultracold atomic Fermi gas confined in a three-dimensional quantum harmonic trap with a BCS pairing interaction. Examining various finite-temperature phase diagrams, we investigate the interplay between the filling of the quantum trap energy levels and the pairing energy. We find that a low (high) filling leads to a large (small) critical population imbalance for the superfluid/normal transition, together with a fully (partially) polarized normal part. We also show that the decrease of the density leads to a changeover of the shape of the superfluid core from an equipotential form to a deformed one. Moreover, we clarify the intrinsic mechanisms that lead to the deformation, providing a unified scenario for phase separation and deformation in a trapped Fermi gas, allowing for a possible interpretation of the apparently controversial experimental findings.

Rigorous Criterion for Reentrance in the Spin-1/2 Ising-Heisenberg Model on Diamond-Like Decorated Bethe Lattices

The ferromagnetic spin-1/2 Ising–Heisenberg model on planar lattices currently attracts a great deal of attention as it may exhibit a variety of interesting phenomena such as a quantum critical point [1, 2], peculiar spontaneous antiferromagnetic long-range order [1] or several unusual spin-liquid ground states [2]. In this work, the spin-1/2 Ising–Heisenberg model on diamond-like decorated Bethe lattices will be treated exactly with the aim to study its ground-state and finite-temperature phase diagrams.

Technicolor in hot and cold phases

We review recent developments on models of dynamical electroweak symmetry breaking. We first consider determination of the conformal window, i.e. the phase diagram, of cold gauge theory and how this can be applied to classify phenomenologically viable models of walking technicolor type. In the second part of the talk we consider finite temperature phase diagram of a generic walking type theory.

Landau-Ginzburg perspective of finite-temperature phase diagrams of a two-component Fermi-Bose mixture

We consider a mixture of two-component Fermi and (one-component) Bose gases under the repulsive Bose-Fermi and attractive Fermi-Fermi interactions. We perform a systematic study of the finite-temperature phase diagrams in the chemical potential space, identifying, using the Landau-Ginzburg theory, the features generic to the phase diagrams within the validity of our model. We apply the theory to explore the physics of correlated BCS pairing among fermions in a tightly confined trap surrounded by a large Bose-Einstein condensate gas.

Phase diagrams of the mixed spin-1 and spin-1/2 Ising–Heisenberg model on the diamond-like decorated Bethe lattice

The ground-state and finite-temperature behavior of the mixed spin-1 and spin-1/2 Ising–Heisenberg model on the diamond-like decorated Bethe lattice is investigated within the framework of two rigorous methods: the decoration-iteration transformation and exact recursion relations. The model under consideration describes a hybrid classical-quantum system consisting of the Ising and Heisenberg spins, which interact among themselves either through the Ising or XXZ Heisenberg nearest-neighbor interaction. Both sublattice magnetizations of the Ising and Heisenberg spins are exactly calculated with the aim to examine phase diagrams, thermal variations of the total and sublattice magnetizations. The finite-temperature phase diagrams form continuous (second-order) phase transition lines only, which exhibit a small reentrant region if the diamond-like decorated Bethe lattice with a sufficiently high coordination number is considered.

Suppression of the critical temperature for superfluidity near the Mott transition

Ultracold atomic gases in optical lattices have proven to be a controllable, tunable and clean implementation of strongly interacting quantum many-body systems. An essential prospect for such quantum simulators is their ability to map out the phase diagram of fundamental many-body model Hamiltonians. However, the results need to be validated first for representative benchmark problems via state-of-the-art numerical methods of quantum many-body theory. Here we present the first ab-initio comparison between experiments and quantum Monte Carlo simulations for strongly interacting Bose gases on a lattice for large systems (up to N = 3e5 particles). The comparison has enabled us to perform thermometry for the interacting quantum gas and to experimentally determine the finite temperature phase diagram for bosonic superfluids in an optical lattice. Our results reveal a downshift of the critical temperature as the transition to the Mott insulator is approached.

N=1Wess-Zumino model ind=3at zero and finite temperature

Supersymmetric renormalization group (RG) flow equations for the effective superpotential of the three-dimensional Wess-Zumino model are derived at zero and non-zero temperature. This model with fermions and bosons interacting via a Yukawa term possesses a supersymmetric analogue of the Wilson-Fisher fixed-point. At zero temperature we determine the phase-transition line in coupling-constant space separating the supersymmetric from the non-supersymmetric phase. At finite temperature we encounter dimensional reduction from 3 to 2 dimensions in the infrared regime. We determine the finite-temperature phase diagram for the restoration of the global $Z_2$-symmetry and show that for temperatures above the $Z_2$ phase transition the pressure obeys the Stefan-Boltzmann law of a gas of massless bosons in 2+1 dimensions.

Ion-trap simulation of the quantum phase transition in an exactly solvable model of spins coupled to bosons

It is known that arrays of trapped ions can be used to efficiently simulate a variety of many-body quantum systems. Here, we show how it is possible to build a model representing a spin chain interacting with bosons which is exactly solvable. The exact spectrum of the model at zero temperature and the ground state properties are studied. We show that a quantum phase transition occurs when the coupling between spins and bosons reaches a critical value, which corresponds to a level crossing in the energy spectrum. Once the critical point is reached, the number of bosonic excitations in the ground state, which can be assumed as an order parameter, starts to be different from zero. The population of the bosonic mode is accompanied by a macroscopic magnetization of the spins. This double effect could represent an useful resource for the phase transition detection since a measure on the phonon can give information about the phase of the spin system. A finite temperature phase diagram is also given in the adiabatic regime.

Modified spin-wave theory with ordering vector optimization: frustrated bosons on the spatially anisotropic triangular lattice

We investigate a system of frustrated hardcore bosons, modeled by an XY antiferromagnet on the spatially anisotropic triangular lattice, using Takahashi's modified spin-wave (MSW) theory. In particular, we implement ordering vector optimization on the ordered reference state of MSW theory, which leads to significant improvement of the theory and accounts for quantum corrections to the classically ordered state. The MSW results at zero temperature compare favorably to exact diagonalization (ED) and projected entangled-pair state (PEPS) calculations. The resulting zero-temperature phase diagram includes a one-dimensional (1D) quasi-ordered phase, a 2D Néel ordered phase and a 2D spiraling ordered phase. Strong indications coming from the ED and PEPS calculations, as well as from the breakdown of MSW theory, suggest that the various ordered or quasi-ordered phases are separated by spin-liquid phases with short-range correlations, in analogy to what has been predicted for the Heisenberg model on the same lattice. Within MSW theory, we also explore the finite-temperature phase diagram. In agreement with the Berezinskii–Kosterlitz–Thouless (BKT) theory, we find that zero-temperature long-range-ordered phases turn into quasi-ordered phases (up to a BKT transition temperature), while zero-temperature quasi-ordered phases become short-range correlated at finite temperature. These results show that, despite its simplicity, MSW theory is very well suited to describing ordered and quasi-ordered phases of frustrated XY spins (or, equivalently, of frustrated lattice bosons) both at zero and finite temperatures. While MSW theory, just as other theoretical methods, cannot describe spin-liquid phases, its breakdown provides a fast and reliable method for singling out Hamiltonians that may feature these intriguing quantum phases. We thus suggest a tool for guiding our search for interesting systems whose properties are necessarily studied with a physical quantum simulator instead of theoretical methods.

Ground state phase diagrams for the mixed Ising 3/2 and 5/2 spin model

We calculate the ground state phase diagrams of a mixed Ising model on a square lattice where spins S (± 3/2, ± 1/2) in one sublattice are in alternating sites with spins Q (± 5/2, ± 3/2, ± 1/2), located on the other sublattice. The Hamiltonian of the model includes first neighbor interactions between the S and Q spins, next-nearest-neighbor interactions between the S spins, and between the Q spins, and crystal field. The topologies of the phase diagrams depend on the values of the parameters in the Hamiltonian. The diagrams show some key features: coexistence between regions, points where two, three, four, five and six states can coexist. Besides being very useful as a way to check the low temperature limit of the finite-temperature phase diagram, often obtained by mean-field theories, the richness of the ground state diagrams for certain combinations of parameters can be used as a guide to explore interesting regions of the finite-temperature phase diagram of the model.

Unbiased Monte Carlo simulations of realistic models: Colossal magnetoresistive manganites

We investigate the one-orbital model for manganites with cooperative phonons and superexchange coupling JAF via large-scale Monte Carlo (MC) simulations. Results for two-orbitals are also briefly discussed. Focusing on an the realistic electronic density n=0.75, a regime of competition between ferromagnetic (FM) metallic and charge-ordered (CO) insulating states was identified in the finite temperature phase diagram. In the vicinity of the associated bicritical point, colossal magnetoresistance (CMR) effects were observed. The CMR magnitude is much larger than recently reported when randomly distributed polarons form the competing insulator. The appearance of CMR is associated with the development of short-distance correlations among polarons, above the spin ordering temperatures, resembling the charge arrangement of the low-temperature CO state. We present calculations of charge-charge correlations as well as typical Monte Carlo snapshots to support this view.

Frustrated further-neighbor antiferromagnetic and electron-hopping interactions in thed=3t−Jmodel: Finite-temperature global phase diagrams from renormalization group theory

The renormalization-group theory of the d=3 tJ model is extended to further-neighbor antiferromagnetic or electron-hopping interactions, including the ranges of frustration. The global phase diagram of each model is calculated for the entire ranges of temperatures, electron densities, and further/first-neighbor interaction strength ratios. In addition to the \tau_{tJ} phase seen in earlier studies of the nearest-neighbor d=3 tJ model, the \tau_{Hb} phase seen before in the d=3 Hubbard model appears both near and away from half-filling. These distinct \tau phases potentially correspond to different (BEC-like and BCS-like) superconducting phases.

Square lattice hard-core bosons within the random phase approximation

Using random phase approximation we build finite-temperature phase diagrams and calculate thermodynamic functions of a square lattice hard-core boson model with nearest (nn) and next-nearest-neighbor (nnn) interactions in terms of equivalent to it an anisotropic spin-1/2 $XXZ$ model in a magnetic field. The system undergoes liquid-solid phase transitions that can be either of the first or second order. Depending on the hopping value and ratio between nn and nnn interactions the system displays two types of critical behavior. The line of the first-order transitions terminates in a bicritical end point inside the solid phase or ends in a tricritical point continuously giving way to the second-order phase transition line. The connection of the hopping and the ratio between the nn and nnn interactions with criticality of the system is investigated. The critical line separating the regions of specific critical behavior is built. Reentrant liquid-solid-liquid phase transitions are found and discussed.

Evolution from BCS to Berezinskii-Kosterlitz-Thouless Superfluidity in One-Dimensional Optical Lattices

We analyze the finite temperature phase diagram of fermion mixtures in one-dimensional optical lattices as a function of interaction strength. At low temperatures, the system evolves from an anisotropic three-dimensional Bardeen-Cooper-Schrieffer (BCS) superfluid to an effectively two-dimensional Berezinskii-Kosterlitz-Thouless (BKT) superfluid as the interaction strength increases. We calculate the critical temperature as a function of interaction strength, and identify the region where the dimensional crossover occurs for a specified optical lattice potential. Finally, we show that the dominant vortex excitations near the critical temperature evolve from multiplane elliptical vortex loops in the three-dimensional regime to planar vortex-antivortex pairs in the two-dimensional regime, and we propose a detection scheme for these excitations.