One-dimensional Spin Research Articles

Open-system spin transport and operator weight dissipation in spin chains

We use non-equilibrium steady states to study the effect of dissipation-assisted operator evolution (DAOE) on the scaling behavior of transport in one-dimensional spin chains. We consider three models in the XXZ family: the XXZ model with staggered anisotropy, which is chaotic; XXZ model with no external field and tunable interaction, which is Bethe ansatz integrable and (in the zero interaction limit) free fermion integrable; and the disordered XY model, which is free-fermion integrable and Anderson localized. We find evidence that DAOE's effect on transport is controlled by its effect on the system's conserved quantities. To the extent that DAOE preserves those symmetries, it preserves the scaling of the system's transport properties; to the extent it breaks those conserved quantities, it pushes the system towards diffusive scaling of transport.

A new general approach for obtaining matrix product operators for spin Hamiltonians with periodic boundary conditions

This article concerns the matrix product operators for one-dimensional spin Hamiltonians under open and periodic boundary conditions. A novel approach called ‘the dynamics of blocks’ is proposed to obtain the matrix product operators in the case of Hamiltonians with periodic boundary conditions. This approach works universally for any Hamiltonian with two-particle as well as single-particle interactions. The main significance of the proposed approach is that, the dimensions of the matrix product operators obtained are the same for both open and periodic boundary conditions. This method gives us a generic way of constructing MPOs for any Hamiltonian with arbitrary neighboring interactions, immaterial of how the interaction strength falls. A general numerical implementation of the ‘dynamics of blocks’ method is also carried out. The DMRG algorithm was implemented, and the ground state eigenvalue was obtained using these MPOs to numerically validate the method.

Separation of quadrupole, spin, and charge across the magnetic phases of a one-dimensional interacting spin-1 gas

We study the low-energy collective properties of a one-dimensional spin-1 Bose gas using bosonization. After giving an overview of the technique, emphasizing the physical aspects, we apply it to the $S=1$ Bose-Hubbard Hamiltonian and find a separation of the quadrupole-spin-charge sectors, confirmed by time--matrix-product states (time-MPS) numerical simulations. Additionally, through the single-particle spectrum, we show the existence of the superfluid--Mott-insulator transition and the point at which the physics are described by a Heisenberg-like Hamiltonian. The magnetic phase diagrams are found for both the superfluid and insulating regimes; the latter is determined by decomposing the complete Heisenberg bilinear-biquadratic Hamiltonian, which describes the Mott insulator, into simpler, effective Hamiltonians. This allows us to keep our methods flexible and transferable to other interesting interacting condensed matter systems.

Exploring dynamical quantum phase transitions in a spin model with deconfined critical point via the quantum steering ellipsoid

The dynamical quantum phase transition (DQPT), which is featured by the nonanalytic behavior of the Loschmidt rate function in the real time evolution, has attracted substantial attention as a valuable theoretical concept for characterizing nonequilibrium states of quantum matter. Although the link between the DQPT and many physical concepts has been established, a thorough understanding of this transition still calls for more studies. In this paper, from the perspective of the quantum steering ellipsoid (QSE), we investigate the DQPTs supported in a one-dimensional spin chain with a deconfined quantum critical point by using the global subspace expansion time-dependent variational principle algorithm. For the quench from the valence-bond-solid phase to the ferromagnetic phase, we find a clear correspondence between the vanishing of the QSE volume and the occurrence of the DQPT. For the quench in the opposite direction, however, the QSE exhibits a rather complicated behavior during the time evolution. We also calculate the quantum entanglement and quantum coherence in the quench processes to unveil the change of the quantum correlations encoded in the QSE picture. These findings could offer a fascinating possibility of revealing DQPTs in a geometrically discernible manner.

Tracking locality in the time evolution of disordered systems

Using local density correlation functions for a one-dimensional spin system, we introduce a correlation function difference (CFD) which compares correlations on a given site between a full system of size $L$ and its restriction to $\ell<L$ sites. We show that CFD provides useful information on transfer of information in quantum many-body systems by considering the examples of ergodic, Anderson, and many-body localized regimes in disordered XXZ spin chain. In the ergodic phase, we find that the propagation of CFD is asymptotically faster than the spin transport but slower than the ballistic propagation implied by the Lieb-Robinson bound. In contrast, in the localized cases, we unravel an exponentially slow relaxation of CFD. Connections between CFD and other observables detecting non-local correlations in the system are discussed.

Simulating the Hamiltonian of dimer atomic spin model of one-dimensional optical lattice on quantum computers

The one-dimensional Ising model with its connections to several physical concepts plays a vital role in comprehension of several principles, phenomena and numerical methods. The Hamiltonian of a coupled one-dimensional dissipative spin system in the presence of magnetic field can be obtained from the Ising model. We simulate the above Hamiltonian by designing a quantum circuit with precise gate measurement and execute with the IBMQ experience platform through different [Formula: see text] states with controlled energy separation where we can check quantum synchronization in a dissipative lattice system. Our result shows the relation between various entangled states, the relation between the different energy separation ([Formula: see text]) with the spin–spin coupling ([Formula: see text]) in the lattice, along with fidelity calculations for several iterations of the model used. We also estimate the ground and first excited energy states of Ising-Hamiltonian using VQE algorithm and investigate the lowest energy values varying the number of layers of ansatz.

Many-body localization in the random-field Heisenberg chain with Dzyaloshinskii-Moriya interaction

We study the one-dimensional spin-1/2 Heisenberg chain with Dzyaloshinskii-Moriya interaction in a random magnetic field using exact diagonalization. In order to obtain many-body mobility edge at infinite temperature, we employ a polynomial filtered Lanczos method that can avoid the fill-in problem when implementing the commonly used shift-and-invert transformation. In stark contrast to the original Heisenberg model, although the localized phase always conforms to Poisson statistics, the ergodic phase exhibits the Gaussian unitary ensemble rather than the Gaussian orthogonal ensemble statistics due to the lack of complex conjugation symmetry. The boundary between the ergodic and localized phases is determined by carefully performing finite-size scalings for the level statistics, entanglement entropy and its standard deviation, as well as fluctuations of the total spin of the system. The two phases are also well distinguished by the full delocalization or localization in the Hilbert space wherein the participation entropies present. To indicate the localized phase in experiment, we propose a scheme for realizing the out-of-time-order correlator on a modern nuclear magnetic resonance quantum simulator.

Effects of Cr doping on the magnetic properties of one-dimensional spin chain system α–CoV2O6

This study investigates the structural and magnetic properties of α–CoV2O6 and Cr doped α–CoV2O6 samples synthesized using a wet chemical method. X-ray diffraction (XRD) measurements and analysis indicate that α–CoV2O6 forms in a monoclinic crystal structure, with lattice parameters a = 9.26 Å, b = 3.50 Å, c = 6.62 Å, β = 111.42°, and α = γ = 90°. The magnetic properties of the compounds were probed using a vibrating sample magnetometer (VSM), by measuring the temperature, T, field, μ0H, and time, t, dependence of magnetization, M. The compounds take on an antiferromagnetic (AFM) order at 0.1 T, with an enhancement of the magnetization below 6.5 K. Cr doping resulted in an enhancement of magnetization below TN. M(μ0H) isotherms show metamagnetic transitions with a 1/3 magnetization plateau for both samples. A large hysteresis is observed for fields less than 5 T and is attributed to frozen metastable, irreversible states. M(T) data at 2.5 T and 5 T shows that the metamagnetic transitions take both compounds from an AFM to an intermediate ferrimagnetic (FI) state and ferromagnetic (FM) state at high fields. No significant changes in TN were observed with Cr doping. Zero-field-cooled (ZFC) and field-cooled (FC) bifurcation was observed for fields between 1 T and 3 T, attributed to spin-glass-like freezing of the samples at TSG. The spin-glass behaviour of the samples was confirmed using the Gabay-Toulouse (G-T) line and M(t) curves.

Gap opening mechanism for correlated Dirac electrons in organic compounds α−(BEDT−TTF)2I3 and α−(BEDT−TSeF)2I3

To determine how electron correlations open a gap in two-dimensional massless Dirac electrons in the organic compounds $\alpha$-(BEDT-TTF)$_2$I$_3$ [$\alpha$-(ET)$_2$I$_3$] and $\alpha$-(BEDT-TSeF)$_2$I$_3$ [$\alpha$-(BETS)$_2$I$_3$], we derive and analyze $ab$ $initio$ low-energy effective Hamiltonians for these two compounds. We find that the horizontal stripe charge ordering opens a gap in the massless Dirac electrons in $\alpha$-(ET)$_2$I$_3$, while an insulating phase without explicit symmetry breaking appears in $\alpha$-(BETS)$_2$I$_3$. We clarify that the combination of the anisotropic transfer integrals and the electron correlations induces a dimensional reduction in the spin correlations, i.e., one-dimensional spin correlations develop in $\alpha$-(BETS)$_2$I$_3$. We show that the one-dimensional spin correlations open a gap in the massless Dirac electrons. Our finding paves the way for opening gaps for massless Dirac electrons using strong electronic correlations.

Viscous flow in a one-dimensional spin-polarized Fermi gas: The role of integrability on viscosity

The transport properties of one-dimensional Fermi gases at low temperatures are often described by the Luttinger liquid (LL) model. However, to study dissipative effects, one needs to examine interactions beyond the LL model. In this work, we provide a simple model that allows for a direct microscopic calculation of the bulk viscosity, namely, the one-dimensional spin polarized $p$-wave Fermi gas. To leading order in the finite interaction strength, we find that the bulk viscosity is finite and consistent with the requirement of scale symmetry. We further show that the bulk viscosity satisfies the Bose-Fermi duality relating the weakly interacting limit of the spin polarized Fermi gas to the strongly interacting limit of the Lieb-Liniger model and vice versa. This work establishes the bulk viscosity to leading order in scale-breaking interactions in both the strongly and weakly interacting limits for both high and low temperatures.

Particle zoo in a doped spin chain: Correlated states of mesons and magnons

It is a widely accepted view that the interplay of spin- and charge-degrees of freedom in doped antiferromagnets (AFMs) gives rise to the rich physics of high-temperature superconductors. Nevertheless, it remains unclear how effective low-energy degrees of freedom and the corresponding field theories emerge from microscopic models, including the $t-J$ and Hubbard Hamiltonians. A promising view comprises that the charge carriers have a rich internal parton structure on intermediate scales, but the interplay of the emergent partons with collective magnon excitations of the surrounding AFM remains unexplored. Here we study a doped one-dimensional spin chain in a staggered magnetic field and demonstrate that it supports a zoo of various long-lived excitations. These include magnons; mesonic pairs of spinons and chargons, along with their ro-vibrational excitations; and tetra-parton bound states of mesons and magnons. We identify these types of quasiparticles in various spectra using DMRG simulations. Moreover, we introduce a strong-coupling theory describing the polaronic dressing and molecular binding of mesons to collective magnon excitations. The effective theory can be solved by standard tools developed for polaronic problems, and can be extended to study similar physics in two-dimensional doped AFMs in the future. Experimentally, the doped spin-chain in a staggered field can be directly realized in quantum gas microscopes.

Magnetic susceptibility of one-dimensional spin chains S(Ni-=SUP=-2+-=/SUP=-)=1 single crystal Y-=SUB=-2-=/SUB=-BaNiO-=SUB=-5-=/SUB=- in the region of 1.85-800 K

The magnetic susceptibility of chi(T) one-dimensional spin chains (OSCs) of a single crystal Y2BaNi05 was first studied in the range of 1.85-800 K. In the region from 800 to ~520 the OCC exhibits Curie-Weiss paramagnetism, in which chi0(T)=C/(T+800), where C is the Curie constant, with an effective magnetic moment of μeff=3.75 μB. With a decrease from 520 to 40 K, the susceptibility changes as a Halden magnet with a gap Delta=117 K, chi(T)=chi0(T)exp(-117/T). Below 40 K chi(T) grows again according to the Curie-Weiss law with μeff=3.75μB, thetai1=-3 K and ni1=9.3·1019 spins S(Ni2+)=1 per mole in a crystal grown in an oxygen-free environment; and thetai2=-1.3 K, and ni2=4.6·1019 spins S(Ni2+)=1 after annealing this crystal to 1000oC in air and its subsequent slow cooling.Such a change in the &amp;quot;impurity&amp;quot; contribution to chi(T) of the OCC is presumably due to a lack of O2 in a significant proportion of the terminal spins in the OCC of a single crystal Keywords: energy gap, SQUID measurements in the region of 1.85-800 K, end spins, breaks in the spin chain.

Фрустрации в основном состоянии разбавленной цепочки Изинга в магнитном поле

The properties of the ground state of one of the simplest models of frustrated magnetic systems, a dilute Ising chain in a magnetic field, are considered for all values of the concentration of charged non-magnetic impurities. An analytical method is proposed for calculating the residual entropy of frustrated states, including states at the boundaries between the phases of the ground state, which is based on the Markov property of the system under consideration and allows direct generalization to other one-dimensional spin models with Ising-type interactions. The properties of local distributions and concentration dependences of the composition, correlation functions, magnetization and entropy of the phases of the ground state of the model are investigated. It is shown that the field-induced transition from the antiferromagnetic ground state to the frustrated one is accompanied by charge ordering and the absence of pseudo-transitions in the dilute Ising chain is proved.

Many-body localization of Z3 Fock parafermions

We study the effects of a random magnetic field on a one-dimensional (1D) spin-1 chain with correlated nearest-neighbor XY interaction. We show that this spin model can be exactly mapped onto the 1D disordered tight-binding model of ${\mathbb{Z}}_{3}$ Fock parafermions (FPFs), exotic anyonic quasiparticles that generalize usual spinless fermions. Thus, we have a peculiar case of a disordered Hamiltonian that despite being bilinear in the creation and annihilation operators, exhibits a many-body localization (MBL) transition owing to the nontrivial statistics of FPFs. This is in sharp contrast to conventional bosonic and fermionic quadratic disordered Hamiltonians that show single-particle (Anderson) localization. We perform finite-size exact diagonalization calculations of level-spacing statistics, fractal dimensions, and entanglement entropy, and provide convincing evidence for the MBL transition at finite disorder strength.

Effects of autocorrelated disorder on the dynamics in the vicinity of the many-body localization transition

The presence of frozen uncorrelated random on-site potential in interacting quantum systems can induce a transition from an ergodic phase to a localized one, the so-called many-body localization. Here we numerically study the effects of autocorrelated disorder on the static and dynamical properties of a one-dimensional many-body quantum system which exhibits many-body localization. Specifically, by means of some standard measures of energy level repulsion and localization of energy eigenstates, we show that a strong degree of correlations between the on-site potentials in the one-dimensional spin-1/2 Heisenberg model leads to suppression of the many-body localization phase, while level repulsion is mitigated for small disorder strengths, although energy eigenstates remain well extended. Our findings are also remarkably manifested in the time domain, on which we put the main emphasis, as shown by the time evolution of experimentally relevant observables, like the return probability and the spin autocorrelation function.

Excitation spectra of one-dimensional spin-1/2 Fermi gas with an attraction

Using an exact Bethe ansatz solution, we rigorously study excitation spectra of the spin-1/2 Fermi gas (called Yang–Gaudin model) with an attractive interaction. Elementary excitations of this model involve particle-hole excitation, hole excitation and adding particles in the Fermi seas of pairs and unpaired fermions. The gapped magnon excitations in the spin sector show a ferromagnetic coupling to the Fermi sea of the single fermions. By numerically and analytically solving the Bethe ansatz equations and the thermodynamic Bethe ansatz equations of this model, we obtain excitation energies for various polarizations in the phase of the Fulde–Ferrell–Larkin–Ovchinnikov-like state. For a small momentum (long-wavelength limit) and in the strong interaction regime, we analytically obtained their linear dispersions with curvature corrections, effective masses as well as velocities in particle-hole excitations of pairs and unpaired fermions. Such a type of particle-hole excitations display a novel separation of collective motions of bosonic modes within paired and unpaired fermions. Finally, we also discuss magnon excitations in the spin sector and the application of Bragg spectroscopy for testing such separated charge excitation modes of pairs and single fermions.

Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems

We provide a detailed comparison between the dynamics of high-temperature spatiotemporal correlation functions in quantum and classical spin models. In the quantum case, our large-scale numerics are based on the concept of quantum typicality, which exploits the fact that random pure quantum states can faithfully approximate ensemble averages, allowing the simulation of spin-$1/2$ systems with up to $40$ lattice sites. Due to the exponentially growing Hilbert space, we find that for such system sizes even a single random state is sufficient to yield results with extremely low noise that is negligible for most practical purposes. In contrast, a classical analog of typicality is missing. In particular, we demonstrate that, in order to obtain data with a similar level of noise in the classical case, extensive averaging over classical trajectories is required, no matter how large the system size. Focusing on (quasi-)one-dimensional spin chains and ladders, we find a remarkably good agreement between quantum and classical dynamics. This applies not only to cases where both the quantum and classical model are nonintegrable, but also to cases where the quantum spin-$1/2$ model is integrable and the corresponding classical $s\to\infty$ model is not. Our analysis is based on the comparison of space-time profiles of the spin and energy correlation functions, where the agreement is found to hold not only in the bulk but also in the tails of the resulting density distribution. The mean-squared displacement of the density profiles reflects the nature of emerging hydrodynamics and is found to exhibit similar scaling for quantum and classical models.

Quantum transport of strongly interacting fermions in one dimension far out of equilibrium

In the study of quantum transport, much has been known about dynamics near thermal equilibrium. However, quantum transport far away from equilibrium is much less well understood---the linear response approximation does not hold for physics far out of equilibrium in general. In this work, motivated by recent cold atom experiments on probing quantum many-body dynamics of a one-dimensional XXZ spin chain, where a transition from ballistic to diffusive dynamics has been established by increasing the interaction strengths, we study the strong interaction limit of the one-dimensional spinless fermion model, which is dual to the XXZ spin chain. We develop a highly efficient computation algorithm for simulating the nonequilibrium dynamics of this system exactly, and examine the nonequilibrium dynamics starting from a density modulation quantum state. We find ballistic transport in this strongly correlated setting and show that a plane-wave description emerges at long-time evolution. We also observe a sharp distinction between transport velocities in short and long times as induced by interaction effects and provide a quantitative interpretation for the long-time transport velocity. We expect our results to shed light on the understanding of the dynamics of the XXZ spin chain in the strong interaction regime.

Band structure of the one-dimensional spin–orbit-coupled Su–Schrieffer–Heeger lattice with [formula omitted]-symmetric onsite imaginary potentials

Energy band structures of one-dimensional non-Hermitian spin–orbit-coupled Su–Schrieffer–Heeger (SSH) model are theoretically investigated, by introducing imaginary potentials with gain and loss effects. It is found that the imaginary potentials can promote the occurrence of PT-symmetry breaking. In the topologically-nontrivial regions, the different imaginary parts of the edge-state energies leads to the different localization degrees of such states. Moreover, gapless phase regions arise between the topologically-nontrivial and -trivial regions, in which edge states are allowed to survive. Therefore, these results are helpful to understand the band-structural and topological properties of PT-symmetric non-Hermitian systems.

Detection of topological quantum phases using dynamical methods

Dynamic and topological phenomena correspond to many new characteristics of matter and have broad application prospects. Focusing on the one-dimensional spin system, different types of topological phases are detected from the viewpoint of non-equilibrium dynamics. The concept of single-site excitation quantum quench is introduced considering the characteristic topological edge state of a topological phase to investigate topological phases. Owing to the protection of edge states against boundary disturbances for a topologically non-trivial phase, the rate function of the Loschmidt echo under quantum quench shows quite different dynamic behaviours during application of single-site excitation on the boundary and interior sites, while no such difference is observed for a topologically trivial phase. This phenomenon also exists on the time-evolved order parameters. The method discussed in this work provides a deep understanding regarding topological protection and a new way to characterise topological phases from the dynamical viewpoints.