Quantum Phase Transition Research Articles

Quantum Phase Transitions in periodically quenched systems

Quantum phase transitions encompass a variety of phenomena that occur in quantum systems exhibiting several possible symmetries. Traditionally, these transitions are explored by continuously varying a control parameter that connects two different symmetry configurations. Here we propose an alternative approach where the control parameter undergoes abrupt and time-periodic jumps between only two values. This approach yields results surprisingly similar to those obtained by the traditional one and may prove experimentally useful in situations where accessing the control parameter is challenging.

Quantum kernels for classifying dynamical singularities in a multiqubit system

Dynamical quantum phase transition is a critical phenomenon involving out-of-equilibrium states and broken symmetries without classical analogy. However, when finite-sized systems are analyzed, dynamical singularities of the rate function can appear, leading to a challenging physical characterization when parameters are changed. Here, we report a quantum support vector machine algorithm that uses quantum Kernels to classify dynamical singularities of the rate function for a multiqubit system. We illustrate our approach using N long-range interacting qubits subjected to an arbitrary magnetic field, which induces a quench dynamics. Inspired by physical arguments, we introduce two different quantum Kernels, one inspired by the ground state manifold and the other based on a single state tomography. Our accuracy and adaptability results show that this quantum dynamical critical problem can be efficiently solved using physically inspiring quantum Kernels. Moreover, we extend our results for the case of time-dependent fields, quantum master equation, and when we increase the number of qubits.

Ground states of planar dipolar rotor chains with recurrent neural networks

In this contribution, we employ a recurrent neural network (RNN) architecture in a variational optimization to obtain the ground state of linear chains of planar, dipolar rotors. We test different local basis sets and discuss their impact on the sign structure of the many-body ground state wavefunction. It is demonstrated that the RNN ansatz we employ is able to treat systems with and without a sign problem in the ground state. For larger chains with up to 50 rotors, accurate properties, such as correlation functions and Binder parameters, are calculated. By employing quantum annealing, we show that precise entanglement properties can be obtained. All these properties allow one to identify a quantum phase transition between a paraelectric and a ferroelectric quantum phase.

Neural-network quantum-state study of the long-range antiferromagnetic Ising chain.

We investigate quantum phase transitions in the transverse field Ising chain with algebraically decaying long-range (LR) antiferromagnetic interactions using the variational Monte Carlo method with the restricted Boltzmann machine employed as a trial wave function ansatz. First, we measure the critical exponents and the central charge through the finite-size scaling analysis, verifying the contrasting observations in the previous tensor network studies. The correlation function exponent and the central charge deviate from the short-range (SR) Ising values at a small decay exponent α_{LR}, while the other critical exponents examined are very close to the SR Ising exponents regardless of α_{LR} examined. However, in the further test of the critical Binder ratio, we find that the universal ratio of the SR limit does not hold for α_{LR}<2, implying a deviation in the criticality. On the other hand, we find evidence of the conformal invariance breakdown in the conformal field theory (CFT) test of the correlation function. The deviation from the CFT description becomes more pronounced as α_{LR} decreases, although a precise breakdown threshold is yet to be determined.

Quantum scaling of the spin lattice relaxation rate in the checkerboard J-Q model

Motivated by recent progress on the experimental realization of proximate deconfined quantum critical point in a frustrated quantum magnet, we study the low-energy spin dynamics of a related checkerboard J-Q model by using quantum Monte Carlo simulations. The ground state of this model undergoes a weakly first-order quantum phase transition with an emergent O(4) symmetry between an antiferromagnetic state and a plaquette valence bond solid. The calculated spin lattice relaxation rate of nuclear magnetic resonance, 1/T1 , exhibits distinct low-temperature behaviors depending on the ground states. With decreasing the temperature, 1/T1 rises up on the antiferromagnetic side, characterizing a crossover to the renormalized classical regime, whereas 1/T1 drops exponentially on the side of valence bond solid, reflecting the gap opening in the plaquette ordered phase. The extracted spin gap scales with the distance to the transition point as a power-law with an exponent φ ≈ 0.3, consistent with the scaling ansatz ϕ=νz with ν ≈ 0.3 and z = 1. Near the quantum phase transition, the temperature dependent 1/T1 shows a broad crossover regime where a universal scaling 1/T1∼Tη with η ≈ 0.6 is found. Our results suggest a quantum scaling regime associated with the emergent enhanced symmetry near this first-order quantum phase transition.

Analytical solution and spectral structure of the two-photon anisotropic Rabi-Stark model

Since the realization of the strong coupling between light and matter in experimental setups, the quantum Rabi model and its generalized models describing the interaction between the boson field and the two-level system have attracted extensive interest again. The study of anisotropic generalized Rabi models enables us to better understand the novel physical properties of the interaction between light and matter in the ultra-strong and deep-strong coupling regions. In this work, the two-photon anisotropic Rabi-Stark model (tpARSM) is analytically solved by using the Bogoliubov operator approach and the su(1, 1) Lie algebra. We derive the G-function, whose zeros give the regular spectrum of the system. By studying the pole structure of the G-function and the coefficients in the function, exceptional solutions, including the first-order quantum phase transition points, doubly degenerate exceptional solutions and nondegenerate exceptional solutions, are obtained. By discussing the spectral structure, we give the conditions for the first-order quantum phase transition of tpARSM. Furthermore, we find that the property that all of the lowest doubly degenerate crossing points in the two-photon Rabi-Stark model have the same energy only holds for the special case of the tpARSM in which the anisotropy parameter is equal to 1. Finally, from the perspective of first-order quantum phase transitions, concise conditions for the ground state energy level to collapse to or escape from the collapse point for the tpARSM are presented. A good understanding of the tpARSM will lay a good foundation for studying the extended two-photon systems involving multiple levels and multiple bosonic modes, and even the relevant open quantum systems.

Critical quantum geometric tensors of parametrically-driven nonlinear resonators

Parametrically driven nonlinear resonators represent a building block for realizing fault-tolerant quantum computation and are useful for critical quantum sensing. From a fundamental viewpoint, the most intriguing feature of such a system is perhaps the critical phenomena, which can occur without interaction with any other quantum system. The non-analytic behaviors of its eigenspectrum have been substantially investigated, but those associated with the ground state wavefunction have largely remained unexplored. Using the quantum ground state geometric tensor as an indicator, we comprehensively establish a phase diagram involving the driving parameter ε and phase ϕ. The results reveal that with the increase in ε, the system undergoes a quantum phase transition from the normal to the symmetry-breaking phase, with the critical point unaffected by ϕ. Furthermore, the critical exponent and scaling dimension are obtained by an exact numerical method, which is consistent with previous works. Our numerical results show that the phase transition falls within the universality class of the quantum Rabi model. This work reveals that the quantum metric and Berry curvature display diverging behaviors across the quantum phase transition.

Scaling and universality at ramped quench dynamical quantum phase transitions

The nonequilibrium dynamics of a periodically driven extended XY model, in the presence of linear time dependent magnetic field, is investigated using the notion of dynamical quantum phase transitions (DQPTs). Along the similar lines to the equilibrium phase transition, the main purpose of this work is to search fundamental concepts such as scaling and universality at the ramped quench DQPTs. We have shown that the critical points of the model, where the gap closing occurs, can be moved by tuning the driven frequency and consequently the presence of or absence of DQPTs can be flexibly controlled by adjusting the driven frequency. We have uncovered that, for a ramp across the single quantum critical point, the critical mode at which DQPTs occur is classified into three regions: the Kibble–Zurek (KZ) region, where the critical mode scales linearly with the square root of the sweep velocity, the pre-saturated (PS) region, and the saturated (S) region where the critical mode makes a plateau versus the sweep velocity. While for a ramp that crosses two critical points, the critical modes disclose just the KZ and PS regions. On the basis of numerical simulations, we find that the dynamical free energy scales linearly with time, as approaches to DQPT time, with the exponent ν=1±0.01 for all sweep velocities and driven frequencies.

Nuclear magnetic resonance studies in a model transverse field Ising system

The suppression of ferroquadrupolar order in TmVO4 in a magnetic field is well-described by the transverse field Ising model, enabling detailed studies of critical dynamics near the quantum phase transition. We describe nuclear magnetic resonance measurements in pure and Y-doped single crystals. The non-Kramers nature of the ground state doublet leads to a unique form of the hyperfine coupling that exclusively probes the transverse field susceptibility. Our results show that this quantity diverges at the critical field, in contrast to the mean-field prediction. Furthermore, we find evidence for quantum critical fluctuations present near Tm-rich regions in Y-doped crystals at levels beyond which long-range order is suppressed, suggesting the presence of quantum Griffiths phases.

Excited-state quantum phase transitions and the entropy of the work distribution in the anharmonic Lipkin-Meshkov-Glick model.

Studying the implications and characterizations of the excited-state quantum phase transitions (ESQPTs) would enable us to understand various phenomena observed in quantum many-body systems. In this work, we delve into the affects and characterizations of the ESQPTs in the anharmonic Lipkin-Meshkov-Glick (LMG) model by means of the entropy of the quantum work distribution. The entropy of the work distribution measures the complexity of the work distribution and behaves as a valuable tool for analyzing nonequilibrium work statistics. We show that the entropy of the work distribution captures salient signatures of the underlying ESQPTs in the model. In particular, a detailed analysis of the scaling behavior of the entropy verifies that it not only acts as a witness of the ESQPTs but also reveals the difference between different types of ESQPTs. We further demonstrate that the work distribution entropy also behaves as a powerful tool for understanding the features and differences of ESQPTs in the energy space. Our results provide further evidence of the usefulness of the entropy of the work distribution for investigating various phase transitions in quantum many-body systems and open up a promising way for experimentally exploring the signatures of ESQPTs.

Unveiling a Family of Dimerized Quantum Magnets, Conventional Antiferromagnets, and Nonmagnets in Ternary Metal Borides.

Dimerized quantum magnets are exotic crystalline materials where Bose-Einstein condensation of magnetic excitations can happen. However, known dimerized quantum magnets are limited to only a few oxides and halides. Here, we unveil 9 dimerized quantum magnets and 11 conventional antiferromagnets in ternary metal borides MTB4 (M = Sc, Y, La, Ce, Lu, Mg, Ca, and Al; T = V, Cr, Mn, Fe, Co, and Ni), where T atoms are arranged in structural dimers. Quantum magnetism in these compounds is dominated by strong antiferromagnetic (AFM) interactions between Cr (Cr and Mn for M = Mg and Ca) atoms within the dimers, with much weaker interactions between the dimers. These systems are proposed to be close to a quantum critical point between a disordered singlet spin-dimer phase, with a spin gap, and the ordered conventional Néel AFM phase. They greatly enrich the materials inventory that allows investigations of the spin-gap phase. Conventional antiferromagnetism in these compounds is dominated by ferromagnetic Mn (Fe for M = Mg and Ca) interactions within the dimers. The predicted stable and nonmagnetic (NM) YFeB4 phase is synthesized and characterized, providing a scarce candidate to study Fe dimers and Fe ladders in borides. The identified quantum, conventional, and NM systems provide a platform with abundant possibilities to tune the magnetic exchange coupling by doping and study the unconventional quantum phase transition and conventional magnetic transitions. This work opens new avenues for studying novel magnetism in borides arising from spin dimers and establishes a theoretical workflow for future searches for dimerized quantum magnets in other families of materials.

Exact zeros of fidelity in finite-size systems as a signature for probing quantum phase transitions.

The fidelity is widely used to detect quantum phase transitions, which is characterized by either a sharp change of fidelity or the divergence of fidelity susceptibility in the thermodynamical limit when the phase-driving parameter is across the transition point. In this work, we unveil that the occurrence of exact zeros of fidelity in finite-size systems can be applied to detect quantum phase transitions. In general, the fidelity F(γ,γ[over ̃]) always approaches zero in the thermodynamical limit, due to the Anderson orthogonality catastrophe, no matter whether the parameters of two ground states (γ and γ[over ̃]) are in the same phase or different phases, and this makes it difficult to distinguish whether an exact zero of fidelity exists by finite-size analysis. To overcome the influence of orthogonality catastrophe, we study finite-size systems with twist boundary conditions, which can be introduced by applying a magnetic flux, and demonstrate that exact zeros of fidelity can be always accessed by tuning the magnetic flux when γ and γ[over ̃] belong to different phases. On the other hand, no exact zero of fidelity can be observed if γ and γ[over ̃] are in the same phase. We demonstrate the applicability of our theoretical scheme by studying concrete examples, including the Su-Schrieffer-Heeger model, Creutz model, and Haldane model. Our work provides a practicable way to detect quantum phase transitions via the calculation of fidelity of finite-size systems.

Quantum materials engineering by structured cavity vacuum fluctuations

A paradigm shift in the research of optical cavities is taking place, focusing on the properties of materials inside cavities. The possibility to affect changes of material groundstates with or without actual photon population inside cavities is an avenue that promises a novel view of materials science and provides a new knob to control quantum phenomena in materials. Here, we present three theoretical scenarios where such groundstate quantum phase transitions are predicted by the coupling of the matter to mere vacuum fluctuations of the cavity, as a realizations of cavity materials engineering in the dark.

Quantum scaling for the metal–insulator transition in a two-dimensional electron system

The quantum phase transition observed experimentally in two-dimensional (2D) electron systems has been a subject of theoretical and experimental studies for almost 30 years. We suggest Gaussian approximation to the mean-field theory of the second-order phase transition to explain the experimental data. Our approach explains self-consistently the universal value of the critical exponent 3/2 (found after scaling measured resistivities on both sides of the transition as a function of temperature) as the result of the divergence of the correlation length when the electron density approaches the critical value. We also provide numerical evidence for the stretched exponential temperature dependence of the metallic phase’s resistivities in a wide range of temperatures and show that it leads to correct qualitative results. Finally, we interpret the phase diagram on the density-temperature plane exhibiting the quantum critical point, quantum critical trajectory and two crossover lines. Our research presents a theoretical description of the seminal experimental results.

Biorthogonal Dynamical Quantum Phase Transitions in Non-Hermitian Systems.

By utilizing biorthogonal bases, we develop a comprehensive framework for studying biorthogonal dynamical quantum phase transitions in non-Hermitian systems. With the help of the previously overlooked associated state, we define the automatically normalized biorthogonal Loschmidt echo. This approach is capable of handling arbitrary non-Hermitian systems with complex eigenvalues and naturally eliminates the negative value of Loschmidt rate obtained without the biorthogonal bases. Taking the non-Hermitian Su-Schrieffer-Heeger model as a concrete example, a 1/2 change of dynamical topological order parameter in biorthogonal bases is observed which is not shown in self-normal bases. Furthermore, we discover that the periodicity of biorthogonal dynamical quantum phase transitions depends on whether the two-level subsystem at the critical momentum oscillates or reaches a steady state.

Quantum Simulation of the Tricritical Ising Model in Tunable Josephson Junction Ladders.

Modern hybrid superconductor-semiconductor Josephson junction arrays are a promising platform for analog quantum simulations. Their controllable and nonsinusoidal energy-phase relation opens the path to implement nontrivial interactions and study the emergence of exotic quantum phase transitions. Here, we propose the analysis of an array of hybrid Josephson junctions defining a two-leg ladder geometry for the quantum simulation of the tricritical Ising phase transition. This transition provides the paradigmatic example of minimal conformal models beyond Ising criticality and its excitations are intimately related to Fibonacci non-Abelian anyons and topological order in two dimensions. We study this superconducting system and its thermodynamic phases based on bosonization and matrix-product-state techniques. Its effective continuous description in terms of a three-frequency sine-Gordon quantum field theory suggests the presence of the targeted tricritical point and the numerical simulations confirm this picture. Our results indicate which experimental observables can be adopted in realistic devices to probe the physics and the phase transitions of the model. Additionally, our proposal provides a useful one-dimensional building block to design exotic topological order in two-dimensional scalable Josephson junction arrays.

Ultra‐Narrow Linewidth Polariton Lasing in Optically Trapped Bose‐Einstein Condensates at Room Temperature

AbstractPolariton lasing via Bose‐Einstein condensation (BEC) provides a peculiar method to achieve low threshold coherent light sources. Until now, the cryogenic operating temperature required for polariton lasers has hampered the development of polaritonics. Here, a novel approach is first reported to realize the ultra‐narrow linewidth polariton lasing under quasi‐3D quantum confinement at room‐temperature (RT). The potential trap landscape is constructed by ring‐shaped optical excitation, wherein the continuum polariton dispersion is modulated into discrete simple harmonic oscillator (SHO) states. The coherent condensation lasing of trapped polaritons occurs beyond the threshold power. Benefiting from the horizontal quantum confinement, the trapped polariton lasing exhibits an ultra‐narrow linewidth (0.7 meV) and excellent quality factor (Q = 3510). Moreover, the second‐order quantum coherence properties of trapped polariton condensation are determined to reveal the quantum phase transition of Bosonic system. The results offer a feasible route for realizing a low‐threshold ultra‐narrow linewidth polariton laser at RT, which significantly facilitates the fabrication of polariton laser and switches on opportunities for future applications.

Quantum Phase Transition in a Modified Jaynes-Cummings Model

We introduce a modified Jaynes-Cummings model with single-photon cavity radiation field but with the atomic system instead of exchanging a single photon as in the Jaynes-Cummings model, it exchanges instead a squeezed photon with squeezing parameter r. This allows us to interpolate between the Rabi model (r = ∞) and the Jaynes-Cummings model (r = 0) by varying r. The model exhibits a quantum phase transition. Accordingly, the quantum phase transition realized in the Rabi model, giving rise to superradiance, also occurs in the Jaynes-Cummings model.

Dynamical quantum phase transitions following a noisy quench

We study how time-dependent energy fluctuations impact the dynamical quantum phase transitions (DQPTs) following a noisy ramped quench of the transverse magnetic field in a quantum Ising chain. By numerically solving the stochastic Schrödinger equation of the mode-decoupled fermionic Hamiltonian of the problem, we identify two generic scenarios: Depending on the amplitude of the noise and the rate of the ramp, the expected periodic sequence of noiseless DQPTs may either be uniformly shifted in time or else replaced by a disarray of closely spaced DQPTs. Guided by an exact noise master equation, we trace the phenomenon to the interplay between noise-induced excitations which accumulate during the quench and the near-adiabatic dynamics of the massive modes of the system. Our analysis generalizes to any one-dimensional fermionic two-band model subject to a noisy quench. Published by the American Physical Society 2024

The dynamical bulk boundary correspondence and dynamical quantum phase transitions in the Benalcazar–Bernevig–Hughes model

In this article we demonstrate that dynamical quantum phase transitions (DQPTs) occur for an exemplary higher order topological insulator, the Benalcazar–Bernevig–Hughes model, following quenches across a topological phase boundary. A dynamical bulk boundary correspondence is also seen both in the eigenvalues of the Loschmidt overlap matrix and the boundary return rate. The latter is found from a finite size scaling analysis for which the relative simplicity of the model is crucial. Contrary to the usual two dimensional case the DQPTs in this model show up as cusps in the return rate, as for a one dimensional model, rather than as cusps in its derivative as would be typical for a two dimensional model. We explain the origin of this behaviour.