Quantum Phase Transition Research Articles

Quantum Criticality with Emergent Symmetry in the Extended Shastry-Sutherland Model.

Motivated by the novel phenomena observed in the layered material SrCu_{2}(BO_{3})_{2}, the Shastry-Sutherland model (SSM) has been extensively studied as the minimal model for SrCu_{2}(BO_{3})_{2}. However, the nature of its quantum phase transition from the plaquette valence-bond solid to antiferromagnetic phase is under fierce debate, posing a challenge to understand the underlying quantum criticality. Via the state-of-the-art tensor network simulations, we study the ground state of the SSM on large-scale size up to 20×20 sites. We identify the continuous transition nature accompanied by an emergent O(4) symmetry between the plaquette valence-bond solid and antiferromagnetic phase, which strongly suggests a deconfined quantum critical point (DQCP). Furthermore, we map out the phase diagram of an extended SSM that can be continuously tuned to the SSM, which demonstrates the same DQCP phenomena along a whole critical line. Our results indicate a compelling scenario for understanding the origin of the proposed proximate DQCP in recent experiments of SrCu_{2}(BO_{3})_{2}.

Scale symmetry breaking and generation of mass at quantum critical points

We study an asymptotically free theory of N relativistic Dirac fermions and a real scalar field coupled by Yukawa and scalar self-interactions in three dimensions using functional renormalisation. In the limit of many fermion flavours, the cubic scalar coupling becomes exactly marginal due to quantum fluctuations, leading to a line of strongly-coupled infrared fixed points. Fermion mass can be generated through a quantum phase transition even if chiral symmetry is absent. The line of fixed points terminates at a critical endpoint due to the loss of vacuum stability. Exactly at the endpoint, scale symmetry is broken spontaneously, leading to the generation of fermion mass. Intriguingly, the absence of chiral symmetry is a prerequisite for the spontaneous generation of fermion mass, and not a consequence thereof. We also highlight close similarities between Gross-Neveu and Gross-Neveu-Yukawa theories at and away from critical points, and establish the large-N equivalence of their functional RG flows and quantum effective actions. Further implications including for conformal field theories are indicated.

Spacing distribution for quantum Rabi models * *Dedicated to Mr. Hiromichi Shinohara, who was instrumental in establishing NTT-IFM, on his 70th birthday.

The asymmetric quantum Rabi model (AQRM) is a fundamental model in quantum optics describing the interaction of light and matter. Besides its immediate physical interest, the AQRM possesses an intriguing mathematical structure which is far from being completely understood. In this paper, we focus on the distribution of the level spacing, the difference between consecutive eigenvalues of the AQRM in the limit of high energies, i.e. large quantum numbers. In the symmetric case, that is the quantum Rabi model (QRM), the spacing distribution for each parity (given by the Z2 -symmetry) is fully clarified by an asymptotic expression derived by de Monvel and Zielinski, though some questions remain for the full spectrum spacing. However, in the general AQRM case, there is no parity decomposition for the eigenvalues. In connection with numerically exact studies and recent theoretical results, we describe the spacing distribution for the AQRM which is characterized by a new type of periodicity and symmetric behavior of the distribution with respect to the bias parameter, reflecting the hidden symmetry of the AQRM. In addition, we observe in the AQRM the excited state quantum phase transition for large values of the bias parameter, analogous to the QRM with large qubit energy, and an internal symmetry of the level spacing distribution for fixed bias. This novel symmetry is independent from the symmetry for half-integer bias and not explained by current theoretical knowledge.

Emergence of quantum Griffiths singularity in disordered TiN thin films

The association of quantum Griffiths singularity (QGS) to the magnetic-field-induced superconductor-metal transition predicts the unconventional diverging behaviour of dynamical critical exponent in low disorder crystalline two-dimensional superconductors. But whether this state exists in the superconducting systems exhibiting superconductor-insulator transition remains elusive. Here, we report the emergence of quantum Griffiths singularity in ultrathin disordered TiN thin films with more than two orders of magnitude variation in their normal state resistance. For both superconductor-metal transition and superconductor-insulator transition types, a diverging critical exponent is observed while approaching the quantum phase transition. Further, the magnetoresistance isotherms obey a direct activated scaling governed by an infinite-randomness fixed critical point. Finally, this work establishes the robustness of the QGS phenomenon towards a wide range of temperature and also towards a wide range of disorder strength as correlated with the normal state resistance.

Adiabatic driving, geometric phases, and the geometric tensor for classical states

We use the Hilbert space formulation of classical mechanics, known as the Koopman–von Neumann formalism, to study adiabatic driving, geometric phases, and the geometric tensor for classical states. In close relation to what happens to a quantum state, a classical Koopman–von Neumann eigenstate will acquire a geometric phase factor expiΦ after a closed variation of the parameters λ in its associated Hamiltonian. The explicit form of Φ is then derived for integrable systems, and its relation with the Hannay angle is shown. Additionally, we use quantum formulas to write an adiabatic gauge potential that generates adiabatic unitary flow between classical eigenstates, and we explicitly show the relationship between the potential and the classical geometric phase. We also define a classical analog of the geometric tensor, thus defining a Fubini–Study metric for classical states, and we use the singularities of the tensor to link the transition from Arnold–Liouville integrability to chaos with some of the mathematical formalism of quantum phase transitions. While the formulas and definitions we use originate in quantum mechanics, all the results found are purely classical, no classical or semiclassical limit is ever taken.

Deconfined quantum criticality of nodal d -wave superconductivity, Néel order, and charge order on the square lattice at half-filling

We consider a SU(2) lattice gauge theory on the square lattice, with a single fundamental complex fermion and a single fundamental complex boson on each lattice site. Projective symmetries of the gauge-charged fermions are chosen so that they match with those of the spinons of the π-flux spin liquid. Global symmetries of all gauge-invariant observables are chosen to match with those of the particle-hole symmetric electronic Hubbard model at half-filling. Consequently, both the fundamental fermion and fundamental boson move in an average background π-flux, their gauge-invariant composite is the physical electron, and eliminating gauge fields in a strong gauge-coupling expansion yields an effective extended Hubbard model for the electrons. The SU(2) gauge theory displays several confining/Higgs phases: a nodal d-wave superconductor, and states with Néel, valence-bond solid, charge, or staggered current orders. There are also a number of quantum phase transitions between these phases that are very likely described by (2+1)-dimensional deconfined conformal gauge theories, and we present large flavor expansions for such theories. These include the phenomenologically attractive case of a transition between a conventional insulator with a charge gap and Néel order, and a conventional d-wave superconductor with gapless Bogoliubov quasiparticles at four nodal points in the Brillouin zone. We also apply our approach to the honeycomb lattice, where we find a bicritical point at the junction of Néel, valence bond solid (Kekulé), and Dirac semimetal phases. Published by the American Physical Society 2024

Quantum phase transition and entanglement entropy in the Dicke model with a squeezed light

Quantum phase transition and entanglement entropy in the Dicke model with a squeezed light

Unscrambling of single-particle wave functions in systems localized through disorder and monitoring

In systems undergoing localization-delocalization quantum phase transitions due to disorder or monitoring, there is a crucial need for robust methods capable of distinguishing phases and uncovering their intrinsic properties. In this paper, we develop a process of finding a Slater determinant representation of free-fermion wave functions that accurately characterizes localized particles, a procedure we dub “unscrambling.” The central idea is to minimize the overlap between envelopes of single-particle wave functions or, equivalently, to maximize the inverse participation ratio of each orbital. This numerically efficient methodology can differentiate between distinct types of wave functions: exponentially localized, power-law localized, and conformal critical, also revealing the underlying physics of these states. The method is readily extendable to systems in higher dimensions. Furthermore, we apply this approach to a more challenging problem involving disordered monitored free fermions in one dimension, where the unscrambling process unveils the presence of a conformal critical phase and a localized area-law quantum Zeno phase. Importantly, our method can also be extended to free fermion systems without particle number conservation, which we demonstrate by estimating the phase diagram of Z2-symmetric disordered monitored free fermions. Our results unlock the potential of utilizing single-particle wave functions to gain valuable insights into the localization transition properties in systems such as monitored free fermions and disordered models. Published by the American Physical Society 2024

Quantum phase transition and critical behavior between the gapless topological phases

Quantum phase transition and critical behavior between the gapless topological phases

Analytical insights into cold bosonic atoms in a zigzag optical lattice: Invariant analysis, exact solutions, and bifurcation analysis using phase portraits

This work delves into the behavior of cold bosonic atoms within a zigzag optical lattice which offers a rich platform for studying quantum many‐body physics and has potential applications in various fields including quantum simulation, quantum computing, and precision measurement. The study aims to derive exact solutions and explore qualitative properties through dynamical analysis. Exact solutions of the nonlinear differential equation model can provide insights into the behavior of bosonic atoms in complex optical lattice configurations, allowing researchers to simulate and study phenomena such as quantum phase transitions, many‐body localization, and exotic states of matter. The invariant analysis has been performed for the first time on the specified equation, yielding a reduced system of equations with forms that are easier to handle. Novel techniques are applied to extract solutions from the reduced system of equations obtained via invariant analysis. The results reveal a rich set of solutions, including various traveling wave solutions and doubly periodic functions in the form of Jacobian elliptic functions. Bifurcation analysis, conducted through phase portraits, provides insights into the system's long‐term behavior under different parameter values. This work contributes to a deeper understanding of the dynamics of cold bosonic atoms in optical lattices via 2D and 3D plots of obtained solutions depicting the change in the behavior of soliton solutions with fractional derivative parameter.

Emergent quantum phase transition of a Josephson junction coupled to a high-impedance multimode resonator

The physics of a single Josephson junction coupled to a resistive environment is a long-standing fundamental problem at the center of an intense debate, strongly revived by the advent of superconducting platforms with high-impedance multimode resonators. Here we investigate the emergent criticality of a junction coupled to a multimode resonator when the number of modes is increased. We demonstrate how the multimode environment renormalizes the Josephson and capacitive energies of the junction so that in the thermodynamic limit the charging energy dominates when the impedance is larger than the resistance quantum and is negligible otherwise, independently from the bare ratio between the two energy scales and the compact or extended nature of the phase of the junction. Via exact diagonalization, we find that the transition surprisingly stems from a level anticrossing involving not the ground state, but the first excited state, whose energy gap vanishes in the thermodynamic limit. We clarify the nature of the two phases by pointing at a different behavior of the ground and excited states and we show that at the transition point the spectrum displays universality not only at low frequencies. In agreement with recent experiments, we reveal striking spectral signatures of the phase transition.

Average coherence and average correlated coherence as indicators of quantum phase transitions in the XY model with staggered Dzyaloshinskii-Moriya interaction

The performance of average coherence (AC) and average correlated coherence (ACC) in detecting quantum phase transitions (QPTs) has been explored by considering the XY model with staggered Dzyaloshinskii-Moriya interaction. By using the quantum renormalization group method, it is shown that the ground-state AC and ACC show either a maximum or a minimum at the QPT point. Moreover, the AC and ACC susceptibilities (i.e. their derivatives with respect to the driving parameter) have two extreme points near the two sides of the QPT point. A finite-scaling analysis reveals that these extreme points tend to the QPT point after several iterations of the renormalization and the susceptibilities at the QPT point become divergent in the thermodynamic limit.

Chebyshev polynomial approach to Loschmidt echo: Application to quench dynamics in two-dimensional quasicrystals.

The understanding of quantum phase transitions in disordered or quasicrystal media is a central issue in condensed matter physics. In this paper we investigate localization properties of the two-dimensional Aubry-André model. We find that the system exhibits self-duality for the transformation between position and momentum spaces at a critical quasiperiodic potential, leading to an energy-independent Anderson transition. Most importantly, we present the implementation of an efficient and accurate algorithm based on the Chebyshev polynomial expansion of the Loschmidt echo, which characterizes the nonequilibrium dynamics of quantum quenched quasiperiodic systems. We analytically prove that the system under quench dynamics displays dynamical quantum phase transitions and further provide numerical verification by computing the polynomial expansion of the Loschmidt echo. Our results may provide insight into the realization of electronic transport in experiments.

Three-dimensional quantum Griffiths singularity in bulk iron-pnictide superconductors

ABSTRACT The quantum Griffiths singularity (QGS) is a phenomenon driven by quenched disorders that break conventional scaling invariance and result in a divergent dynamic critical exponent during quantum phase transitions (QPT). While this phenomenon has been well-documented in low-dimensional conventional superconductors and in three-dimensional (3D) magnetic metal systems, its presence in 3D superconducting systems and in unconventional high-temperature superconductors (high-Tc SCs) remains unclear. In this study, we report the observation of robust QGS in the superconductor-metal transition (SMT) of both quasi-2D and 3D anisotropic unconventional high-Tc superconductor CaFe1-xNixAsF (x <5%) bulk single crystals, where the QGS states persist to up to 5.3 K. A comprehensive quantum phase diagram is established that delineates the 3D anisotropic QGS of SMT induced by perpendicular and parallel magnetic fields. Our findings reveal the universality of QGS in 3D superconducting systems and unconventional high-Tc SCs, thereby substantially expanding the range of applicability of QGS.

Magnon interactions in a moderately correlated Mott insulator

Quantum fluctuations in low-dimensional systems and near quantum phase transitions have significant influences on material properties. Yet, it is difficult to experimentally gauge the strength and importance of quantum fluctuations. Here we provide a resonant inelastic x-ray scattering study of magnon excitations in Mott insulating cuprates. From the thin film of SrCuO2, single- and bi-magnon dispersions are derived. Using an effective Heisenberg Hamiltonian generated from the Hubbard model, we show that the single-magnon dispersion is only described satisfactorily when including significant quantum corrections stemming from magnon-magnon interactions. Comparative results on La2CuO4 indicate that quantum fluctuations are much stronger in SrCuO2 suggesting closer proximity to a magnetic quantum critical point. Monte Carlo calculations reveal that other magnetic orders may compete with the antiferromagnetic Néel order as the ground state. Our results indicate that SrCuO2—due to strong quantum fluctuations—is a unique starting point for the exploration of novel magnetic ground states.

Bath-Engineering Magnetic Order in Quantum Spin Chains: An Analytic Mapping Approach.

Dissipative processes can drive different magnetic orders in quantum spin chains. Using a nonperturbative analytic mapping framework, we systematically show how to structure different magnetic orders in spin systems by controlling the locality of the attached baths. Our mapping approach reveals analytically the impact of spin-bath couplings, leading to the suppression of spin splittings, bath dressing and mixing of spin-spin interactions, and emergence of nonlocal ferromagnetic interactions between spins coupled to the same bath, which become long ranged for a global bath. Our general mapping method can be readily applied to a variety of spin models: we demonstrate (i)a bath-induced transition from antiferromagnetic (AFM) to ferromagnetic ordering in a Heisenberg spin chain, (ii)AFM to extended Neel phase ordering within a transverse-field Ising chain with pairwise couplings to baths, and (iii)a quantum phase transition in the fully connected Ising model. Our method is nonperturbative in the system-bath coupling. It holds for a variety of non-Markovian baths and it can be readily applied towards studying bath-engineered phases in frustrated or topological materials.

Intertwined quantum phase transitions in the zirconium and niobium isotopes

Nuclei in the A ≈ 100 region exhibit intricate shape-evolution and configuration crossing signatures. Exploring both even–even and their adjacent odd-mass nuclei gives further insight on the emergence of deformation and shape-phase transitions. We employ the algebraic frameworks of the interacting boson model with configuration mixing and the new interacting boson-fermion model with configuration mixing in order to investigate the even–even zirconium with neutron number 52–70 (40Zr) and odd-mass niobium (41Nb) isotopes with 52–62. We compare between the evolution in energy levels, configuration and symmetry content of the wave functions, two neutron separation energies and E2 transition rates, alongside comparison with the experimental data. The comparisons between the two chains of isotopes denote the occurrence of two types of QPTs, a crossing of normal and intruder configurations (named Type II QPT), and a shape-evolution of the intruder configuration (named Type I QPT). The latter QPT begins from spherical shape to axially deformed rotor in the Zr isotopes and from weak to strong coupling scenario in the Nb isotopes. This occurrence, named intertwined quantum phase transitions (IQPTs), in the even–even Zr chain is thus demonstrated to persists when coupling a proton to the boson core for the odd-mass Nb chain, even as deformation increases.

Degeneracy in excited-state quantum phase transitions of two-level bosonic models and its influence on system dynamics

Degeneracy in excited-state quantum phase transitions of two-level bosonic models and its influence on system dynamics

Lieb-Robinson correlation function for the quantum transverse-field Ising model

The Lieb-Robinson correlation function is the norm of a commutator between local operators acting on separate subsystems at different times. This provides a useful state-independent measure for characterizing the specifically quantum interaction between spatially separated qubits. The finite propagation velocity for this correlator defines a “light cone” of quantum influence. We calculate the Lieb-Robinson correlation function for one-dimensional qubit arrays described by the transverse-field Ising model. Direct calculations of this correlation function have been limited by the exponential increase in the size of the state space with the number of qubits. We introduce a technique that avoids this barrier by transforming the calculation to a sum over Pauli walks which results in linear scaling with system size. We can then explore propagation in arrays of hundreds of qubits and observe the effects of the quantum phase transition in the system. We observe the emergence of two distinct velocities of propagation: a correlation front velocity, which is affected by the phase transition, and the Lieb-Robinson velocity which is not. The correlation front velocity is equal to the maximum group velocity of single quasiparticle excitations. The Lieb-Robinson velocity describes the extreme leading edge of correlations when the value of the correlation function itself is still very small. For the semi-infinite chain of qubits at the quantum critical point, we derive an analytical result for the correlation function. Published by the American Physical Society 2024

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.