Finite-temperature Properties Research Articles

Effective field theories and finite-temperature properties of zero-dimensional superradiant quantum phase transitions

The existence of zero-dimensional superradiant quantum phase transitions seems inconsistent with conventional statistical physics. This work clarifies this apparent inconsistency. We demonstrate the corresponding effective field theories and finite-temperature properties of light-matter interacting systems, and show how this zero-dimensional quantum phase transition occurs. We first focus on the Rabi model, which is a minimum model that hosts a superradiant quantum phase transition. With the path-integral method, we derive the imaginary-time action of the photon degrees of freedom. We also define a dynamical critical exponent as the rescaling between the temperature and the photon frequency, and perform dimensional analysis to the effective action. The dynamical critical exponent shows that the effective theory of the Rabi model is a free scalar field, where a true second-order quantum phase transition emerges. These results are also verified by numerical simulations of imaginary-time correlation functions of the order parameter. Furthermore, we also generalize this method to the Dicke model. Our results make the zero-dimensional superradiant quantum phase transition compatible with conventional statistical physics, and pave the way to understand it in the perspective of effective field theories. Published by the American Physical Society 2024

Coupled cluster finite temperature simulations of periodic materials via machine learning

Density functional theory is the workhorse of materials simulations. Unfortunately, the quality of results often varies depending on the specific choice of the exchange-correlation functional, which significantly limits the predictive power of this approach. Coupled cluster theory, including single, double, and perturbative triple particle-hole excitation operators, is widely considered the ‘gold standard' of quantum chemistry as it can achieve chemical accuracy for non-strongly correlated applications. Because of the high computational cost, the application of coupled cluster theory in materials simulations is rare, and this is particularly true if finite-temperature properties are of interest for which molecular dynamics simulations have to be performed. By combining recent progress in machine learning models with low data requirements for energy surfaces and in the implementation of coupled cluster theory for periodic materials, we show that chemically accurate simulations of materials are practical and could soon become significantly widespread. As an example of this numerical approach, we consider the calculation of the enthalpy of adsorption of CO2 in a porous material.

Towards the high-throughput prediction of finite-temperature properties using the quasi-harmonic approximation

Lattice dynamics calculations within the quasi-harmonic approximation (QHA) provide an infrastructure for modelling the finite-temperature properties of periodic solids at a modest computational cost. With the recent widespread interest in materials discovery by data mining, a database of computed finite-temperature properties would be highly desirable. In this work we provide a first step toward this goal with a comparative study of the accuracy of five exchange-correlation functionals, spanning the local density approximation (LDA), generalised-gradient approximation (GGA) and meta-GGA levels of theory, for predicting the properties of ten Group 1, 2 and 12 binary metal oxides. We find that the predictions are bounded by the LDA, which tends to underestimate lattice parameters and cell volumes relative to experiments, but yields the most accurate results for bulk moduli, expansion coefficients and Grüneisen parameters, and the PBE GGA, which shows the opposite behaviour. The PBEsol GGA gives the best overall predictions of the lattice parameters and volumes whilst also giving relatively reliable results for other properties. Our results demonstrate that, given a suitable choice of functional, a variety of finite-temperature properties can be predicted with useful accuracy, and hence that high-throughout QHA calculations are technically feasible.

Non-collinear magnetic atomic cluster expansion for iron

The Atomic Cluster Expansion (ACE) provides a formally complete basis for the local atomic environment. ACE is not limited to representing energies as a function of atomic positions and chemical species, but can be generalized to vectorial or tensorial properties and to incorporate further degrees of freedom (DOF). This is crucial for magnetic materials with potential energy surfaces that depend on atomic positions and atomic magnetic moments simultaneously. In this work, we employ the ACE formalism to develop a non-collinear magnetic ACE parametrization for the prototypical magnetic element Fe. The model is trained on a broad range of collinear and non-collinear magnetic structures calculated using spin density functional theory. We demonstrate that the non-collinear magnetic ACE is able to reproduce not only ground state properties of various magnetic phases of Fe but also the magnetic and lattice excitations that are essential for a correct description of finite temperature behavior and properties of crystal defects.

Finite-temperature properties of the easy-axis Heisenberg model on frustrated lattices

Finite-temperature properties of the easy-axis Heisenberg model on frustrated lattices

A theoretical investigation on the structural stability, superconductivity, and optical and thermodynamic properties of Ir2P under pressure.

The potential applications of Ir2P are promising due to its desirable hardness, but its fundamental properties are still not fully understood. In this study, we present a systematic investigation of Ir2P's structural, electronic, superconducting, optical, and thermodynamic properties of Ir2P under pressure. Our calculations show that Ir2P has a Fm3̄m structure at ambient pressure, which matches well with experimental data obtained from high-pressure synchrotron X-ray diffraction. As pressure increases, a transition from the Fm3̄m to the I4/mmm phase occurs at 103.4 GPa. The electronic structure and electron-phonon coupling reveal that the Fm3̄m and I4/mmm phases of Ir2P are superconducting materials with superconducting transition temperatures of 2.51 and 0.89 K at 0 and 200 GPa, respectively. The optical properties of Ir2P indicate that it has optical conductivity in the infrared, visible, and ultraviolet regions. Additionally, we observed that the reflectivity R(ω) of Ir2P is higher than 76% in the 25-35 eV energy range at different pressures, which suggests that it could be used as a reflective coating. We also explored the finite-temperature thermodynamic properties of Ir2P, including the Debye temperature, the first and second pressure derivatives of the isothermal bulk modulus, and the thermal expansion coefficient up to 2000 K using the quasi-harmonic Debye model. Our findings offer valuable insights for engineers to design better devices.

Unravelling abnormal in-plane stretchability of two-dimensional metal-organic frameworks by machine learning potential molecular dynamics.

Two-dimensional (2D) metal-organic frameworks (MOFs) hold immense potential for various applications due to their distinctive intrinsic properties compared to their 3D analogues. Herein, we designed a highly stable NiF2(pyrazine)2 2D MOF in silico with a two-dimensional periodic wine-rack architecture. Extensive first-principles calculations and molecular dynamics (MD) simulations based on a newly developed machine learning potential (MLP) revealed that this 2D MOF exhibits huge in-plane Poisson's ratio anisotropy. This results in anomalous negative in-plane stretchability, as evidenced by an uncommon decrease in its in-plane area upon the application of uniaxial tensile strain, which makes this 2D MOF particularly attractive for flexible wearable electronics and ultra-thin sensor applications. We further demonstrated the unique capability of MLP to accurately predict the finite-temperature properties of MOFs on a large scale, exemplified by MLP-MD simulations with a dimension of 28.2 × 28.2 nm2, relevant to the length scale experimentally attainable for the fabrication of MOF films.

Canonical formulation for the thermodynamics of sln-invariant integrable spin chains

Integrable quantum spin chains display distinctive physical properties making them a laboratory to test and assess different states of matter. The study of the finite temperature properties is possible by use of the thermodynamic Bethe ansatz, however at the expense of dealing with non-linear integral equations for, in general, infinitely many auxiliary functions. The definition of an alternative finite set of auxiliary functions allowing for the complete description of their thermodynamic properties at finite temperature and fields has been elusive. Indeed, in the context of sln-invariant models satisfactory auxiliary functions have been established only for n≤4. In this paper we take a step further by proposing a systematic approach to generate finite sets of auxiliary functions for sln-invariant models. We refer to this construction as the canonical formulation. The numerical efficiency is illustrated for n=5, for which we present some of the thermodynamic properties of the corresponding spin chain.

Finite-temperature properties of PbTiO3 by molecular dynamics simulations

PbTiO 3 is a prototypical ferroelectric perovskite that is known to undergo a temperature driven ferroelectric tetragonal to paraelectric cubic phase transition, but the understanding of some key phenomena and associated mechanisms underlying this transition remains unclear. Here, using molecular dynamics simulations based on first-principles effective Hamiltonian, we show the behaviors of the phase transition temperature Tc and adiabatic temperature change ΔT of PbTiO3 under an external electric field and tensile stress along the [001] direction. Our results show that the electric field E induces rising Tc via a linear relationTc∝ 0.3083E, rendering the phase transition to go from first-order with thermal hysteresis to second-order without thermal hysteresis above ∼200 kV/cm; meanwhile, a maximum electrocaloric response ΔTmax∼34 K is obtained under E=500 kV/cm. Moreover, external stress (σz) causes rising Tc via a linear relationTc∝160σz and improves the electrocaloric response ΔTmax when combined with the electric field. The present results offer insights into the physical processes and mechanisms that dictate finite-temperature properties of ferroelectric perovskite oxides, laying a foundation for further exploration of this intriguing class of materials.

Robust Extraction of Thermal Observables from State Sampling and Real-Time Dynamics on Quantum Computers

Simulating properties of quantum materials is one of the most promising applications of quantum computation, both near- and long-term. While real-time dynamics can be straightforwardly implemented, the finite temperature ensemble involves non-unitary operators that render an implementation on a near-term quantum computer extremely challenging. Recently, Lu, Bañuls and Cirac \cite{Lu2021} suggested a "time-series quantum Monte Carlo method" which circumvents this problem by extracting finite temperature properties from real-time simulations via Wick's rotation and Monte Carlo sampling of easily preparable states. In this paper, we address the challenges associated with the practical applications of this method, using the two-dimensional transverse field Ising model as a testbed. We demonstrate that estimating Boltzmann weights via Wick's rotation is very sensitive to time-domain truncation and statistical shot noise. To alleviate this problem, we introduce a technique that imposes constraints on the density of states, most notably its non-negativity, and show that this way, we can reliably extract Boltzmann weights from noisy time series. In addition, we show how to reduce the statistical errors of Monte Carlo sampling via a reweighted version of the Wolff cluster algorithm. Our work enables the implementation of the time-series algorithm on present-day quantum computers to study finite temperature properties of many-body quantum systems.

Energy storage properties of ferroelectric nanocomposites

An atomistic effective Hamiltonian technique is used to investigate the finite-temperature energy storage properties of a ferroelectric nanocomposite consisting of an array of ${\mathrm{BaTiO}}_{3}$ nanowires embedded in a ${\mathrm{SrTiO}}_{3}$ matrix, for electric field applied along the long axis of the nanowires. We find that the energy density versus temperature curve adopts a nonlinear, mostly temperature-independent response when the system exhibits phases possessing an out-of-plane polarization and vortices, while the energy density more linearly increases with temperature when the nanocomposite either only possesses vortices (and thus no spontaneous polarization) or is in a paraelectric and paratoroidic phase for its equilibrium state. Ultrahigh-energy density up to $\ensuremath{\simeq}141 \mathrm{J}/{\mathrm{cm}}^{3}$ and an ideal 100% efficiency are also predicted in this nanocomposite. A phenomenological model, involving a coupling between polarization and toroidal moment, is further proposed to interpret these energy density results.

Efficient low temperature Monte Carlo sampling using quantum annealing

Quantum annealing is an efficient technology to determine ground state configurations of discrete binary optimization problems, described through Ising Hamiltonians. Here we show that—at very low computational cost—finite temperature properties can be calculated. The approach is most efficient at low temperatures, where conventional approaches like Metropolis Monte Carlo sampling suffer from high rejection rates and therefore large statistical noise. To demonstrate the general approach, we apply it to spin glasses and Ising chains.

Some finite temperature and ground state properties of high-Tc superconductivity within the planar t-J-U model

In high-Tc materials, considering pair hopping and on-site pairing of electrons, presence of two electrons at a site following Pauli exclusion principle (a t-J-U model) is relevant. Considering this novelty, within a two-dimensional (2D) t-J-U Hamiltonian, some thermodynamic and ground state properties of high-Tc cuprates at various hole doping concentrations (〈h〉) have been investigated. Any theory based on perturbation approximation is inapplicable in strongly correlated electron systems, therefore, Lanczos method of exact diagonalization on a square cluster (tilted) of 8-sites is followed. Results show that double occupancy (δ) is maximum for hole concentration 〈h〉 = 0.25 and increases at a particular temperature T = T(U). Local moment shows the opposite behavior. Spin-spin correlation is negative between nearest-neighbor sites, confirming antiferromagnetic nature of the system. It appears that on-site Coulomb repulsion (U/t ≥ 6.0) destabilizes the superconducting ground state. In the system, antiferromagnetism (AF) and superconductivity are seen to coexist. A uniform distribution of charges is seen with increasing on-site Coulomb repulsion (U), which results in constant electron–electron correlation.

Phases of a 10-D holographic hard wall model

In this article, we study the finite temperature properties of a 10-D version of a hardwall model for QCD. Introducing fundamental matter via probe D7-branes and separate cutoffs rm and rg for the branes and the bulk, we present a detailed exploration of the phases for varying temperature and quark mass. Finite thermodynamic quantities are calculated using the procedure of holographic renormalization and used to characterize the phases. Finally, by fitting glueball and vector meson masses, we show how a unique phase diagram can be isolated.

Anharmonic thermo-elasticity of tungsten from accelerated Bayesian adaptive biasing force calculations with data-driven force fields

The elastic properties of tungsten, a ubiquitous material in future energy systems, are investigated up to its melting temperature by means of a data-driven approach. The proposed workflow combines machine learning of the force field and enhanced sampling of the crystalline structure. While the machine learning force field achieves the accuracy of ab initio calculations, its implementation in sampling methods is often limited due to its high computational cost, which is commonly a few orders of magnitude larger than that of traditional potentials. To overcome this limitation, we propose a fast and robust Bayesian sampling scheme aiming at estimating the fully anharmonic free energy of crystalline solids with the help of an improved adaptive biasing force method. This method performs a thermodynamic integration from a harmonic reference system, wherein zero frequencies associated with the periodic boundaries are screened off. The proposed sampling method drastically improves the speed of convergence and overall accuracy. We demonstrate the efficiency of the improved method by calculating the second order derivatives of the free energy, such as the elastic constants, which are performed almost 100 times faster than with the standard methods. The proposed method enables the prediction of the elastic properties of tungsten in the range of temperatures that cannot be investigated experimentally, from 2100 K to the melting temperature. The accuracy and numerical efficiency of the proposed strategy open up many avenues for the reliable prediction of finite-temperature properties of materials, such as the relative stability of structural defects and elastic constants.

Exploring finite temperature properties of materials with quantum computers

Thermal properties of nanomaterials are crucial to not only improving our fundamental understanding of condensed matter systems, but also to developing novel materials for applications spanning research and industry. Since quantum effects arise at the nano-scale, these systems are difficult to simulate on classical computers. Quantum computers can efficiently simulate quantum many-body systems, yet current quantum algorithms for calculating thermal properties of these systems incur significant computational costs in that they either prepare the full thermal state on the quantum computer, or they must sample a number of pure states from a distribution that grows with system size. Canonical thermal pure quantum (TPQ) states provide a promising path to estimating thermal properties of quantum materials as they neither require preparation of the full thermal state nor require a growing number of samples with system size. Here, we present an algorithm for preparing canonical TPQ states on quantum computers. We compare three different circuit implementations for the algorithm and demonstrate their capabilities in estimating thermal properties of quantum materials. Due to its increasing accuracy with system size and flexibility in implementation, we anticipate that this method will enable finite temperature explorations of relevant quantum materials on near-term quantum computers.

Monte Carlo studies of noncollinear magnetic phases in multiferroic Cu2OSeO3

Monte Carlo simulations based on a first-principles-derived Hamiltonian are conducted to study the finite-temperature properties of chiral-lattice multiferroic insulator ${\mathrm{Cu}}_{2}{\mathrm{OSeO}}_{3}$. The use of this numerical technique (i) reveals basic features of the phase diagram as a function of temperature and external magnetic field, including the long-range helical phase at low temperature and zero magnetic field and the skyrmion lattice phase, in which skyrmions are arranged in a two-dimensional hexagonal lattice, and (ii) leads to the discovery of an overlooked vortex lattice phase in a narrow pocket of the phase diagram near the fluctuations' disordered-helical phase transition. The scheme also provides strong numerical evidence that the transition to a helical state in ${\mathrm{Cu}}_{2}{\mathrm{OSeO}}_{3}$ is of first order driven by critical fluctuations.

Variational quantum simulation of thermal statistical states on a superconducting quantum processer

Quantum computers promise to solve finite-temperature properties of quantum many-body systems, which is generally challenging for classical computers due to high computational complexities. Here, we report experimental preparations of Gibbs states and excited states of Heisenberg XX and XXZ models by using a 5-qubit programmable superconducting processor. In the experiments, we apply a hybrid quantum–classical algorithm to generate finite temperature states with classical probability models and variational quantum circuits. We reveal that the Hamiltonians can be fully diagonalized with optimized quantum circuits, which enable us to prepare excited states at arbitrary energy density. We demonstrate that the approach has a self-verifying feature and can estimate fundamental thermal observables with a small statistical error. Based on numerical results, we further show that the time complexity of our approach scales polynomially in the number of qubits, revealing its potential in solving large-scale problems.

CASM — A software package for first-principles based study of multicomponent crystalline solids

CASM is a software package that enables first-principles based studies of crystalline materials. It has been designed to treat coupled chemical, mechanical, vibrational, and magnetic degrees of freedom to determine ground state and finite temperature properties of crystals. The symmetry of the underlying parent crystal structure is used to enumerate perturbations of the parent crystal structure and generate derivative structures which can be input to first-principles calculations in order to explore the ground state energy landscape. CASM algorithmically constructs cluster expansions that fully couple discrete and continuous degrees of freedom, and generates highly efficient code to evaluate the cluster expansion basis functions. Widely used machine learning methods are integrated for fitting expansion coefficients to first-principle calculations. The fully parameterized cluster expansions can be combined with (kinetic) Monte Carlo methods to calculate finite temperature thermodynamic and kinetic properties. CASM Alloy Manager identifies distinct parent crystal structures in an alloy system, creating individual projects for each, and integrating the results. The integrated infrastructure facilitates the linkage between first-principles statistical mechanics predictions with higher length scale computational methods, such as phase field simulations. CASM projects are designed to be easy to share in repositories, to re-use, and to extend to include additional chemical species or types of degrees of freedom.

Finite-temperature properties of extended Nagaoka ferromagnetism: Ordering processes and precursor of a quantum phase transition between itinerant ferromagnetic and Mott antiferromagnetic states

We study finite-temperature properties of a Hubbard model including sites of a particle bath, which was proposed as a microscopic model to show itinerant ferromagnetism at finite electron density. We use direct numerical methods, such as exact diagonalization and random vector methods. The temperature dependence of quantities is surveyed in the full range of the temperature. We find that the specific heat has several peaks, which correspond to ordering processes in different energy scales. In particular, magnetic correlations develop at very low temperature. The system exhibits an itinerant ferromagnetic state or an antiferromagnetic state of the Mott insulator depending on the chemical potential of the particle bath and the Coulomb interaction. From a microscopic viewpoint, the competition between these two types of magnetic states causes a peculiar ordering process of local spin correlations. Some local ferromagnetic correlations are found to be robust, which indicates that the ferromagnetic correlation originates from the motion of itinerant electrons in a short-range cluster.