Quantum XY Model Research Articles

Universality in the tripartite information after global quenches: (generalised) quantum XY models

We consider the Rényi-α tripartite information {I}_3^{left(alpha right)} of three adjacent subsystems in the stationary state emerging after global quenches in noninteracting spin chains from both homogeneous and bipartite states. We identify settings in which {I}_3^{left(alpha right)} remains nonzero also in the limit of infinite lengths and develop an effective quantum field theory description of free fermionic fields on a ladder. We map the calculation into a Riemann-Hilbert problem with a piecewise constant matrix for a doubly connected domain. We find an explicit solution for α = 2 and an implicit one for α > 2. In the latter case, we develop a rapidly convergent perturbation theory that we use to derive analytic formulae approximating {I}_3^{left(alpha right)} with outstanding accuracy.

Noise-Induced Quantum Synchronization.

Synchronization is a widespread phenomenon in science and technology. Here, we study noise-induced synchronization in a quantum spin chain subjected to local Gaussian white noise. We demonstrate stable (anti)synchronization between the endpoint magnetizations of a quantum XY model with transverse field of arbitrary length. Remarkably, we show that noise applied to a single spin suffices to reach stable (anti)synchronization, and find that the two synchronized end spins are entangled. We additionally determine the optimal noise amplitude that leads to the fastest synchronization along the chain, and further compare the optimal synchronization speed to the fundamental Lieb-Robinson bound for information propagation.

Exactly solvable one-dimensional quantum models with gamma matrices.

In this paper we write exactly solvable generalizations of one-dimensional quantum XY and Ising-like models by using 2^{d}-dimensional gamma matrices as the degrees of freedom on each site. We show that these models result in quadratic Fermionic Hamiltonians with Jordan-Wigner-like transformations. We illustrate the techniques using a specific case of four-dimensional gamma matrices and explore the quantum phase transitions present in the model.

Powerful method to evaluate the mass gaps of free-particle quantum critical systems

We present a numerical method for the evaluation of the mass gap, and the low-lying energy gaps, of a large family of free-fermionic and free-parafermionic quantum chains. The method is suitable for some generalizations of the quantum Ising and XY models with multispin interactions. We illustrate the method by considering the Ising quantum chains with uniform and random coupling constants. The mass gaps of these quantum chains are obtained from the largest root of a characteristic polynomial. We also show that the Laguerre bound, for the largest root of a polynomial, used as an initial guess for the largest root in the method, gives us estimates for the mass gaps sharing the same leading finite-size behavior as the exact results. This opens an interesting possibility of obtaining precise critical properties very efficiently which we explore by studying the critical point and the paramagnetic Griffiths phase of the quantum Ising chain with random couplings. In this last phase, we obtain the effective dynamical critical exponent as a function of the distance-to-criticality. Finally, we compare the mass gap estimates derived from the Laguerre bound and the strong-disorder renormalization-group method. Both estimates require comparable computational efforts, with the former having the advantage of being more accurate and also being applicable away from infinite-randomness fixed points. We believe this method is a relevant tool for tackling critical quantum chains with and without quenched disorder.

Distribution of entanglement with variable range interactions

Distribution of quantum entanglement is investigated for an anisotropic quantum XY model with variable range interactions and in the presence of a uniform transverse magnetic field. We report the possibility of qualitative growth in entanglement between distant sites with an increase in the range of interactions that vary either exponentially or polynomially as the distance between the sites increases. Interestingly, we find that such entanglement enhancement is not ubiquitous and is dependent on the factorization points, a specific set of system parameters where the zero-temperature state of the system is fully separable. In particular, we observe that at zero-temperature, when the system parameters are chosen beyond the pair of factorization points, the increments in entanglement length due to variable range interactions are more pronounced compared to the situation when the parameters lie in between the factorization points. By employing the sum of all the bipartite entanglements with respect to a single site, we also show that the shareability of the bipartite entanglements is constrained, thereby establishing their monogamous nature. Furthermore, we note that the factorization points get reallocated depending on the laws of interaction fall-offs and provide an ansatz for the same. We reveal that the temperature at which the canonical equilibrium state becomes entangled from an unentangled one increases with the increase in the range of interactions, thereby demonstrating enhanced robustness in entanglement against temperature in the presence of long-range interactions and only when the system parameters are chosen between the pair of factorization points. We apply an energy-based entanglement witness to provide a justification to the observed robustness with temperature.

Uhlmann fidelity and fidelity susceptibility for integrable spin chains at finite temperature: exact results

We derive the exact expression for the Uhlmann fidelity between arbitrary thermal Gibbs states of the quantum XY model in a transverse field with finite system size. Using it, we conduct a thorough analysis of the fidelity susceptibility of thermal states for the Ising model in a transverse field. We compare the exact results with a common approximation that considers only the positive-parity subspace, which is shown to be valid only at high temperatures. The proper inclusion of the odd parity subspace leads to the enhancement of maximal fidelity susceptibility in the intermediate range of temperatures. We show that this enhancement persists in the thermodynamic limit and scales quadratically with the system size. The correct low-temperature behavior is captured by an approximation involving the two lowest many-body energy eigenstates, from which simple expressions are obtained for the thermal susceptibility and specific heat.

Exact thermal properties of free-fermionic spin chains

An exact description of integrable spin chains at finite temperature is provided using an elementary algebraic approach in the complete Hilbert space of the system. We focus on spin chain models that admit a description in terms of free fermions, including paradigmatic examples such as the one-dimensional transverse-field quantum Ising and XY models. The exact partition function is derived and compared with the ubiquitous approximation in which only the positive parity sector of the energy spectrum is considered. Errors stemming from this approximation are identified in the neighborhood of the critical point at low temperatures. We further provide the full counting statistics of a wide class of observables at thermal equilibrium and characterize in detail the thermal distribution of the kink number and transverse magnetization in the transverse-field quantum Ising chain.

Phase diagram and quantum criticality of a non-Hermitian XY model with a complex transverse field

We study a one dimensional non-Hermitian quantum XY model with a complex transverse field, where the imaginary transverse field can be generated by three-level atoms with spontaneous decay. Many-body spectrum can be obtained analytically. The phase diagram in thermodynamical limit indicates that the imaginary transverse field induces non-Hermitian degeneracy and shrinks the ferromagnetic phase for anisotropic interaction. We also analyze the effect of imaginary field on quantum criticality through ground state geometry phase. It causes a shift of transition point but does not change the order of phase transition in anisotropic interaction region. However, the phase transition is related to the original Hermitian degeneracy in anisotropic interaction region, which indicates that the imaginary transverse field cannot change phase boundary and critical behavior.

Site-Monotonicity Properties for Reflection Positive Measures with Applications to Quantum Spin Systems

We consider a general statistical mechanics model on a product of local spaces and prove that, if the corresponding measure is reflection positive, then several site-monotonicity properties for the two-point function hold. As an application, we derive site-monotonicity properties for the spin–spin correlation of the quantum Heisenberg antiferromagnet and XY model, we prove that spin-spin correlations are point-wise uniformly positive on vertices with all odd coordinates—improving previous positivity results which hold for the Cesàro sum. We also derive site-monotonicity properties for the probability that a loop connects two vertices in various random loop models, including the loop representation of the spin O(N) model, the double-dimer model, the loop O(N) model and lattice permutations, thus extending the previous results of Lees and Taggi (2019).

Machine-learning study using improved correlation configuration and application to quantum Monte Carlo simulation.

We use the Fortuin-Kasteleyn representation-based improved estimator of the correlation configuration as an alternative to the ordinary correlation configuration in the machine-learning study of the phase classification of spin models. The phases of classical spin models are classified using the improved estimators, and the method is also applied to the quantum Monte Carlo simulation using the loop algorithm. We analyze the Berezinskii-Kosterlitz-Thouless (BKT) transition of the spin-1/2 quantum XY model on the square lattice. We classify the BKT phase and the paramagnetic phase of the quantum XY model using the machine-learning approach. We show that the classification of the quantum XY model can be performed by using the training data of the classical XY model.

Response of entanglement to annealed vis-à-vis quenched disorder in quantum spin models

We investigate bipartite entanglement in random quantum XY models at equilibrium. Depending on the intrinsic time scales associated with equilibration of the random parameters and measurements associated with observation of the system, we consider two distinct kinds of disorder, namely annealed and quenched. We conduct a comparative study of the effects of disorder on nearest-neighbor entanglement, when the nature of randomness changes from being annealed to quenched. We find that entanglement properties of the annealed and quenched systems are drastically different from each other. This is realized by identifying the regions of parameter space in which the nearest-neighbor state is entangled, and the regions where a disorder-induced enhancement of entanglement —order-from-disorder— is obtained. We also analyze the response of the quantum phase transition point of the ordered system with the infusion of disorder.

Phase transition in phase transition lines of quantum XY model

Phase transitions in quantum systems, including symmetry breaking and topological types, always associate with gap closing and opening. We analyze the topological features of the quantum phase boundary of the XY model in a transverse magnetic field. Based on the results from graphs in the auxiliary space, we find that gapless ground states at boundary have different topological characters. On the other hand, in the framework of Majorana representation, the Majorana lattice is shown to be two coupled SSH chains. The analysis of the quantum fidelity for the Majorana eigen vector, which is shown to be identical to the square of that for ground states of the XY model, indicates the signature of the gapless phase transition (GPT). Furthermore analytical and numerical results for second-order derivative of groundstate energy density show that such a GPT obeys scaling behavior.

Staggered Long-Range Order for Diluted Quantum Spin Models

We study an annealed site diluted quantum XY model with spin Sin tfrac{1}{2}{mathbb {N}}. We find regions of the parameter space where, in spite of being a priori favourable for a densely occupied state, phases with staggered occupancy occur at low temperatures.

Phase boundaries in an alternating-field quantum XY model with Dzyaloshinskii-Moriya interaction: Sustainable entanglement in dynamics

We report all phases and corresponding critical lines of the quantum anisotropic transverse XY model with Dzyaloshinskii-Moriya (DM) interaction along with uniform and alternating transverse magnetic fields (ATXY) by using appropriately chosen order parameters. We prove that when DM interaction is weaker than the anisotropy parameter, it has no effect at all on the zero-temperature states of the XY model with uniform transverse magnetic field which is not the case for the ATXY model. However, when DM interaction is stronger than the anisotropy parameter, we show appearance of a new gapless phase - a chiral phase - in the XY model with uniform as well as alternating field. We further report that first derivatives of nearest neighbor two-site entanglement with respect to magnetic fields can detect all the critical lines present in the system. We also observe that the factorization surface at zero-temperature present in this model without DM interaction becomes a volume on the introduction of the later. We find that DM interaction can generate bipartite entanglement sustainable at large times, leading to a proof of ergodic nature of bipartite entanglement in this system, and can induce a transition from non-monotonicity of entanglement with temperature to a monotonic one.

Quantum simulation scheme of two-dimensional xy-model Hamiltonian with controllable coupling

We study a scheme of quantum simulator for two-dimensional xy-model Hamiltonian. Previously the quantum simulator for a coupled cavity array spin model has been explored, but the coupling strength is fixed by the system parameters. In the present scheme several cavity resonators can be coupled with each other simultaneously via an ancilla qubit. In the two-dimensional Kagome lattice of the resonators the hopping of resonator photonic modes gives rise to the tight-binding Hamiltonian which in turn can be transformed to the quantum xy-model Hamiltonian. We employ the transmon as an ancilla qubit to achieve in situ controllable xy-coupling strength.

Properties and application of SO(3) Majorana representation of spin: Equivalence with Jordan-Wigner transformation and exact Z2 gauge theories for spin models

We explore the properties of the SO(3) Majorana representation of spin. Based on its nonlocal nature, it is shown that there is an equivalence between the SO(3) Majorana representation and the Jordan-Wigner transformation in one and two dimensions. From the relation between the SO(3) Majorana representation and one-dimensional Jordan-Wigner transformation, we show that application of the SO(3) Majorana representation usually results in ${Z}_{2}$ gauge structure. Based on lattice Chern-Simons gauge theory, it is shown that the anticommuting link variables in the SO(3) Majorana representation make it equivalent to an operator form of compact ${\text{U(1)}}_{1}$ Chern-Simons Jordan-Wigner transformation in 2D. As examples of its application, we discuss two spin models, namely the quantum XY model on a honeycomb lattice and the ${90}^{\ensuremath{\circ}}$ compass model on a square lattice. It is shown that under the SO(3) Majorana representation both spin models can be exactly mapped into ${Z}_{2}$ gauge theory of spinons, with the standard form of ${Z}_{2}$ Gauss law constraint.

A machine learning approach to the Berezinskii-Kosterlitz-Thouless transition in classical and quantum models

The Berezinskii-Kosterlitz-Thouless transition is a very specific phase transition where all thermodynamic quantities are smooth. Therefore, it is difficult to determine the critical temperature in a precise way. In this paper we demonstrate how neural networks can be used to perform this task. In particular, we study how the accuracy of the transition identification depends on the way the neural networks are trained. We apply our approach to three different systems: (i) the classical XY model, (ii) the phase-fermion model, where classical and quantum degrees of freedom are coupled and (iii) the quantum XY model.

Topological phase transition of the anisotropic XY model with Dzyaloshinskii-Moriya interaction

Within the real space renormalization group we obtain the phase portrait of the anisotropic quantum XY model on square lattice in presence of Dzyaloshinskii-Moriya (DM) interaction. The model is characterized by two parameters, $\lambda$ corresponding to XY anisotropy, and $D$ corresponding to the strength of DM interaction. The flow portrait of the model is governed by two global Ising-Kitaev attractors at $(\lambda=\pm1,D=0)$ and a repeller line, $\lambda=0$. Renormalization flow of concurrence suggests that the $\lambda=0$ line corresponds to a topological phase transition. The gap starts at zero on this repeller line corresponding to super-fluid phase of underlying bosons; and flows towards a finite value at the Ising-Kitaev points. At these two fixed points the spin fields become purely classical, and hence the resulting Ising degeneracy can be interpreted as topological degeneracy of dual degrees of freedom. The state of affairs at the Ising-Kitaev fixed point is consistent with the picture of a p-wave pairing of strength $\lambda$ of Jordan-Wigner fermions coupled with Chern-Simons gauge fields.

Benford analysis of quantum critical phenomena: First digit provides high finite-size scaling exponent while first two and further are not much better

Benford's law is an empirical edict stating that the lower digits appear more often than higher ones as the first few significant digits in statistics of natural phenomena and mathematical tables. A marked proportion of such analyses is restricted to the first significant digit. We employ violation of Benford's law, up to the first four significant digits, for investigating magnetization and correlation data of paradigmatic quantum many-body systems to detect cooperative phenomena, focusing on the finite-size scaling exponents thereof. We find that for the transverse field quantum XY model, behavior of the very first significant digit of an observable, at an arbitrary point of the parameter space, is enough to capture the quantum phase transition in the model with a relatively high scaling exponent. A higher number of significant digits do not provide an appreciable further advantage, in particular, in terms of an increase in scaling exponents. Since the first significant digit of a physical quantity is relatively simple to obtain in experiments, the results have potential implications for laboratory observations in noisy environments.

Anomalous quantum critical spin dynamics in YFe2Al10

We report results of a muon spin relaxation ($\mu$SR) study of YFe$_2$Al$_{10}$, a quasi-2D nearly-ferromagnetic metal in which unconventional quantum critical behavior is observed. No static Fe$^{2+}$ magnetism, with or without long-range order, is found down to 19~mK\@. The dynamic muon spin relaxation rate~$\lambda$ exhibits power-law divergences in temperature and magnetic field, the latter for fields that are too weak to affect the electronic spin dynamics directly. We attribute this to the proportionality of $\lambda(\omega_\mu,T)$ to the dynamic structure factor~$S(\omega_\mu,T)$, where $\omega_\mu \approx 10^5$--$10^7~\mathrm{s}^{-1}$ is the muon Zeeman frequency. These results suggest critical divergences of $S(\omega_\mu,T)$ in both temperature and frequency. Power-law scaling and a 2D dissipative quantum XY (2D-DQXY) model both yield forms for $S(\omega,T)$ that agree with neutron scattering data ($\omega \approx 10^{12}~\mathrm{s}^{-1}$). Extrapolation to $\mu$SR frequencies agrees semi-quantitatively with the observed temperature dependence of $\lambda(\omega_\mu,T)$, but predicts frequency independence for $\omega_\mu \ll T$ in extreme disagreement with experiment. We conclude that the quantum critical spin dynamics of YFe$_2$Al$_{10}$ are not well understood at low frequencies.