XYZ Spin Research Articles

Explicit Construction of Local Conserved Quantities in the XYZ Spin-1/2 Chain.

We present a rigorous explicit expression for an extensive number of local conserved quantities in the XYZ spin-1/2 chain with general coupling constants. All the coefficients of operators in each local conserved quantity are calculated. We also confirm that our result can be applied to the case of the XXZ chain with a magnetic field in the z-axis direction.

The quantum speed limit time of a two-qubit XYZ spin chain with intrinsic decoherence

We study the quantum speed limit (QSL) time of the two-qubit XYZ spin chain model with the influence of intrinsic decoherence. We show that the intrinsic decoherence can suppress the evolution of this system, no matter what initial states the two qubits start from. The investigation of entanglement reveals that quantum correlation is the physical reason for the acceleration of the system. In addition, we also demonstrate that for different initial states, external magnetic field may have opposite influence on QSL time and it mainly derives from the inhibition of entanglement as magnetic field increases.

Quantum Berezinskii–Kosterltz–Thouless transition for topological insulator

ABSTRACTWe consider the interacting helical liquid system at the one-dimensional edge of a two-dimensional topological insulator, coupled to an external magnetic field and s-wave superconductor and map it to an XYZ spin chain system. This model undergoes quantum Berezinskii–Kosterlitz–Thouless (BKT) transition with two limiting conditions. We derive the renormalization group (RG) equations explicitly and also present the flow lines behavior. We also present the behavior of RG flow lines based on the exact solution. We observe that the physics of Majorana fermion zero modes and the gaped Ising-ferromagnetic phase, which appears in a different context. We observe that the evidence of gapless helical Luttinger liquid phase as a common non-topological quantum phase for both quantum BKT transitions. We explain analytically and physically that there is no Majorana-Ising transition. In the presence of chemical potential, the system shows the commensurate to incommensurate transition.

Exact Nonequilibrium Steady State of Open XXZ/XYZ Spin-1/2 Chain with Dirichlet Boundary Conditions.

We investigate a dissipatively driven XYZ spin-1/2 chain in the Zeno limit of strong dissipation, described by the Lindblad master equation. The nonequilibrium steady state is expressed in terms of a matrix product ansatz using novel site-dependent Lax operators. The components of Lax operators satisfy a simple set of linear recurrence equations that generalize the defining algebraic relations of the quantum group U_{q}(sl_{2}). We reveal connection between the nonequilibrium steady state of the nonunitary dynamics and the respective integrable model with edge magnetic fields, described by coherent unitary dynamics.

Inhomogeneous matrix product ansatz and exact steady states of boundary-driven spin chains at large dissipation.

We find novel site-dependent Lax operators in terms of which we demonstrate exact solvability of a dissipatively driven XYZ spin-1/2 chain in the Zeno limit of strong dissipation, with jump operators polarizing the boundary spins in arbitrary directions. We write the corresponding nonequilibrium steady state using an inhomogeneous matrix product ansatz, where the constituent matrices satisfy a simple set of linear recurrence relations. Although these matrices can be embedded into an infinite-dimensional auxiliary space, we have verified that they cannot be simultaneously put into a tridiagonal form, not even in the case of axially symmetric (XXZ) bulk interactions and general nonlongitudinal boundary dissipation. We expect our results to have further fundamental applications for the construction of nonlocal integrals of motion for the open XYZ model with arbitrary boundary fields, or the eight-vertex model.

Enhancement in the performance of a quantum battery by ordered and disordered interactions

Considering ground state of a quantum spin model as the initial state of the quantum battery, we show that both ordered and disordered interaction strengths play a crucial role to increase the extraction of power from it. In particular, we demonstrate that exchange interactions in the xy-plane and in the z-direction, leading to the XYZ spin chain, along with local charging field in the x-direction substantially enhance the efficiency of the battery compared to the model without interactions. Moreover, such an advantage in power obtained due to interactions is almost independent of the system size. We find that the behavior of the power, although measured during dynamics, can faithfully mimic the equilibrium quantum phase transitions present in the model. We observe that with the proper tuning of system parameters, initial state prepared at finite temperature can generate higher power in the battery than that obtained with zero-temperature. Finally, we report that defects or impurities, instead of reducing the performance, can create larger amount of quenched averaged power in the battery in comparison with the situation when the initial state is produced from the spin chain without disorder, thereby showing the disorder-induced order in dynamics.

Anomalous Behavior of Magnetic Susceptibility Obtained by Quench Experiments in Isolated Quantum Systems.

We examine how the magnetic susceptibility obtained by the quench experiment on isolated quantum systems is related to the isothermal and adiabatic susceptibilities defined in thermodynamics. Under the conditions similar to the eigenstate thermalization hypothesis, together with some additional natural ones, we prove that for translationally invariant systems the quench susceptibility as a function of wave vector k is discontinuous at k=0. Moreover, its values at k=0 and the k→0 limit coincide with the adiabatic and the isothermal susceptibilities, respectively. We give numerical predictions on how these particular behaviors can be observed in experiments on the XYZ spin chain with tunable parameters, and how they deviate when the conditions are not fully satisfied.

On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions

The transfer matrix of the square-lattice eight-vertex model on a strip with vertical lines and open boundary conditions is investigated. It is shown that for vertex weights that obey the relation and appropriately chosen K-matrices this transfer matrix possesses the remarkably simple, non-degenerate eigenvalue . For positive vertex weights, is shown to be the largest transfer-matrix eigenvalue. The corresponding eigenspace is equal to the space of the ground states of the Hamiltonian of a related XYZ spin chain. An essential ingredient in the proofs is the supersymmetry of this Hamiltonian.

Unification of integrability in supersymmetric gauge theories

A four-dimensional analog of Chern-Simons theory produces integrable lattice models from Wilson lines and surface operators. We show that this theory describes a quasi-topological sector of maximally supersymmetric Yang-Mills theory in six dimensions, topologically twisted and subjected to an \Omega-deformation. By realizing the six-dimensional theory in string theory and applying dualities, we unify various phenomena in which the eight-vertex model and the XYZ spin chain, as well as variants thereof, emerge from supersymmetric gauge theories.

Magnetic Properties of an Antiferromagnetic Spin-1/2 XYZ Model in the Presence of Different Magnetic Fields: Finite-Size Effects of Inhomogeneity Property**Supported by the ICTP Affiliated Center Program AF-04, and the CS MES RA in the frame of the research project No. SCS 18T-1C155

Magnetic and thermodynamic properties of the anisotropic XYZ spin-1/2 finite chain under both homogeneous and inhomogeneous magnetic fields are theoretically studied at low temperature. Using exact diagonalization method (ED), we study the magnetization, magnetic susceptibility, and specific heat of the model characterized in terms of the finite correlation length in the presence of three different magnetic fields including longitudinal, transverse, and transverse staggered magnetic fields. The magnetization, susceptibility, and the specific heat of the model are investigated under two conditions separately: (i) When the model is putted in the presence of homogeneous magnetic fields. (ii) When finite inhomogeneities are considered for all applied magnetic fields in the Hamiltonian. We show that for the finite-size XYZ chains at low temperature, the evident magnetization plateaus gradually convert to their counterpart quasi-plateaus when the transverse magnetic field increases. Moreover, the influence of the transverse and staggered transverse magnetic fields, and their corresponding inhomogeneities on the magnetization process, magnetic susceptibility, and specific heat are reported in detail. Our exact results illustrate that by altering the inhomogeneity parameters, magnetization plateaus gradually convert to their counterpart quasi-plateaus. The specific heat manifests Schottky-type maximum, double-peak, and triple-peak, as well as, transformation between them by varying considered inhomogeneity parameters in the Hamiltonian.

Variational Quantum MonteCarlo Method with a Neural-Network Ansatz for Open Quantum Systems.

The possibility to simulate the properties of many-body open quantum systems with a large number of degrees of freedom (d.o.f.) is the premise to the solution of several outstanding problems in quantum science and quantum information. The challenge posed by this task lies in the complexity of the density matrix increasing exponentially with the system size. Here, we develop a variational method to efficiently simulate the nonequilibrium steady state of Markovian open quantum systems based on variational MonteCarlo methods and on a neural network representation of the density matrix. Thanks to the stochastic reconfiguration scheme, the application of the variational principle is translated into the actual integration of the quantum master equation. We test the effectiveness of the method by modeling the two-dimensional dissipative XYZ spin model on a lattice.

Entanglement and Measurement-induced quantum correlation in Heisenberg spin models

Correlation beyond entanglement is a subject of interest in quantum information. Here we showed the existence of quantum correlation without entanglement in Heisenberg XYZ spin model with external magnetic field, using different versions of measurement-induced nonlocality. Maximally entangled states are shown to possess maximum correlation.

Characterization of Majorana-Ising phase transition in a helical liquid system

Abstract We map an interacting helical liquid system, coupled to an external magnetic field and s-wave superconductor, to an XYZ spin system, and it undergoes Majorana-Ising transition by tuning of parameters. In the Majorana state lowest excitation gap decays exponentially with system size, and the system has degenerate ground state in the thermodynamic limit. On the contrary, the gap opens in the Ising phase even in the thermodynamic limit. We study various criteria to characterize the transition, such as edge spin correlation with its neighbor C ( r = 1 ) , local susceptibility χ i , superconducting order parameter of edge spin P ( r = 1 ) , and longitudinal structure factor S ( k ) . All these criteria lead to the same critical value of parameters for Majorana-Ising phase transition in the thermodynamic limit. We study the entanglement spectrum of the reduced density matrix of the helical liquid system. The system shows finite Schmidt gap and non-degeneracy of the entanglement spectrum in the Ising limit. The Schmidt gap closes in the Majorana state, and all the eigenvalues are either doubly or multiply degenerate.

Energy transport in a disordered spin chain with broken U(1) symmetry: Diffusion, subdiffusion, and many-body localization

We explore the physics of the disordered XYZ spin chain using two complementary numerical techniques: exact diagonalization (ED) on chains of up to 17 spins, and time-evolving block decimation (TEBD) on chains of up to 400 spins. Our principal findings are as follows. First, the clean XYZ spin chain shows ballistic energy transport for all parameter values that we investigated. Second, for weak disorder there is a stable diffusive region that persists up to a critical disorder strength that depends on the XY anisotropy. Third, for disorder strengths above this critical value energy transport becomes increasingly subdiffusive. Fourth, the many-body localization transition moves to significantly higher disorder strengths as the XY anisotropy is increased. We discuss these results, and their relation to our current physical picture of subdiffusion in the approach to many-body localization.

Quantum-memory-assisted entropic uncertainty in two-qubit Heisenberg XYZ chain with Dzyaloshinskii–Moriya interactions and effects of intrinsic decoherence

Quantum-memory-assisted entropic uncertainty relation (QMA-EUR) in two-qubit Heisenberg XYZ spin chain model with Dzyaloshinskii–Moriya (DM) interaction has been investigated. The paper shows that the DM interactions and the spin interactions alone x, y, z directions can efficiently suppress the entropic uncertainty of Pauli observables ( $$\sigma _{x}$$ and $$\sigma _{z}$$ ), even make the entropic uncertainty close to zero. As well, it is pointed out that the entropic uncertainty reaches to zero at very low temperature, starts to increase with temperature after a threshold, and generally becomes constant at a fixed value. We also verified the Bob’s uncertainty about Alice’s measurement outcomes is anticorrelated with the sum of the accessible information of observer. Furthermore, the decoherence conditions including dephasing and noisy environments are considered. For the fixed initial state, the entropic uncertainty of the XYZ model with DM interaction in z-direction are independent of spin–spin coupling $$J_z$$ and the anisotropy parameter $$\varDelta $$ . In the dephasing environment, the evolutions of entropic uncertainty and its lower bound $$U_{B}$$ oscillate with the time and saturates at a finite value, and this value is varied with the purity parameter r of initial state. In the noisy environment, the entropic uncertainty and its lower bound monotonically increase with the time and will be stable at value 2 quickly. This is because the combined effects of the DM interaction and the decoherence force the various initial entanglement states to oscillate into an identical state, regardless of the value of $$D_{z}$$ and the parameter r of initial state.

Indirect magnetic interaction mediated by Fermi arc and boundary reflection near Weyl semimetal surface

We theoretically investigate the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between magnetic impurities distributed in the vicinity of the surface of a Weyl semimetal. Contrary to previous studies, we further take into account the influence of interplay of the Fermi arc and bulk states, and interface refection. It is shown that the RKKY pattern is significantly mediated by the Fermi-arc surface state along with the interface reflection. The Fermi-arc surface state mediates the RKKY interaction by interfering with the bulk states. The resulting interference contribution in the short-range impurity distance R is comparable in magnitude to the bulk-band contribution and even dominates the latter near the surface. It either enhances or weakens the bulk contribution, depending on the relative orientation of impurities and Fermi energy. More importantly, for the long-range impurity distance the interference term dominates in that it can prolong the decay rate from the original bulk R−5-law to R−2 (R−3) for finite (zero) Fermi energy. The interface reflection not only enhances the magnitude of the RKKY interaction and changes its anisotropy from the original XXZ to XYZ or Ising spin model, but also generates extra twisted RKKY terms parallel to the line connecting Weyl nodes, lacked in the scenario without the interface effect. They originate from the interaction between the impurity and the mirror image of the other impurity. We further analyze in detail the spatial anisotropy of the decay rate and beating pattern. These findings provide a deeper insight into surface magnetic interaction mediated by Weyl fermions.

Driven-dissipative quantum Monte Carlo method for open quantum systems

We develop a real-time Full Configuration Interaction Quantum Monte Carlo approach for the modeling of driven-dissipative open quantum systems. The method enables stochastic sampling of the Liouville-von-Neumann time evolution of the density matrix, thanks to a massively parallel algorithm, thus providing estimates of observables on the non-equilibrium steady state. We present the underlying theory, and introduce initiator technique and importance sampling to reduce the statistical error. Finally, we demonstrate the efficiency of our approach by applying it to the driven- dissipative two-dimensional XYZ spin model on lattice.

Exact phase boundaries and topological phase transitions of the XYZ spin chain.

Within the block spin renormalization group, we give a very simple derivation of the exact phase boundaries of the XYZ spin chain. First, we identify the Ising order along x[over ̂] or y[over ̂] as attractive renormalization group fixed points of the Kitaev chain. Then, in a global phase space composed of the anisotropy λ of the XY interaction and the coupling Δ of the Δσ^{z}σ^{z} interaction, we find that the above fixed points remain attractive in the two-dimesional parameter space. We therefore classify the gapped phases of the XYZ spin chain as: (1) either attracted to the Ising limit of the Kitaev-chain, which in turn is characterized by winding number ±1, depending on whether the Ising order parameter is along x[over ̂] or y[over ̂] directions; or (2) attracted to the charge density wave (CDW) phases of the underlying Jordan-Wigner fermions, which is characterized by zero winding number. We therefore establish that the exact phase boundaries of the XYZ model in Baxter's solution indeed correspond to topological phase transitions. The topological nature of the phase transitions of the XYZ model justifies why our analytical solution of the three-site problem that is at the core of the present renormalization group treatment is able to produce the exact phase boundaries of Baxter's solution. We argue that the distribution of the winding numbers between the three Ising phases is a matter of choice of the coordinate system, and therefore the CDW-Ising phase is entitled to host appropriate form of zero modes. We further observe that in the Kitaev-chain the renormalization group flow can be cast into a geometric progression of a properly identified parameter. We show that this new parameter is actually the size of the (Majorana) zero modes.

Entanglement dynamics in Heisenberg spin chains coupled to a dissipative environment at finite temperature

We consider a finite one-dimensional Heisenberg XYZ spin chain under the influence of dissipative Lindblad environment obeying the Born-Markovian constrain in presence of an external magnetic field. We apply both closed and open boundary conditions at zero and finite temperature. We present an exact numerical solution for the Lindblad master equation of the system in the Liouville space. we find that, in the free spin chain (in absence of any environment), the entanglement at all ranges evolve in time in a non-uniform oscillatory form that changes significantly depending on the initial state, system size and the spatial anisotropy. The oscillatory behavior is suppressed once the system is coupled to the environment. Furthermore, the asymptotic behavior of the entanglement, nearest neighbor and beyond, in the system under the influence of the environment at zero temperature is very sensitive to the x-y spatial anisotropy, which causes them to reach either a zero or a finite sustainable steady state value regardless of the initial state of the system. The anisotropy in the $z-$direction may enhance the entanglement depending on the interplay with the magnetic field applied in the same direction. As the temperature is raised, the steady state of the short range entanglements is found to be robust within very small non-zero temperature range, which depends critically on the spatial anisotropy of the system. The entanglement at each range depends differently on the spatial anisotropy. Moreover, the end to end entanglement transfer time and speed through the open boundary chain vary significantly based on the degree of anisotropy and the temperature of the environment.

Disordered XYZ spin chain simulations using the spectrum bifurcation renormalization group

We study the disordered XYZ spin chain using the recently developed Spectrum Bifurcation Renormalization Group (SBRG) numerical method. With strong disorder, the phase diagram consists of three many body localized (MBL) spin glass phases. We argue that, with sufficiently strong disorder, these spin glass phases are separated by marginally many-body localized (MBL) critical lines. We examine the critical lines of this model by measuring the entanglement entropy and Edwards-Anderson spin glass order parameter, and find that the critical lines are characterized by an effective central charge c'=ln2. Our data also suggests continuously varying critical exponents along the critical lines. We also demonstrate how long-range mutual information can distinguish these phases.