Quantum Heisenberg Spin Glass Research Articles

Exact Numerical Solution of the Fully Connected Classical and Quantum Heisenberg Spin Glass.

We present the mean field solution of the quantum and classical Heisenberg spin glasses, using the combination of a high precision numerical solution of the Parisi full replica symmetry breaking equations and a continuous time quantum MonteCarlo algorithm. We characterize the spin glass order and its low-energy excitations down to zero temperature. The Heisenberg spin glass has a rougher energy landscape than its Ising analog, and exhibits a very slow temperature evolution of its dynamical properties. We extend our analysis to the doped, metallic Heisenberg spin glass, which displays unexpectedly slow spin dynamics, reflecting the proximity to the melting quantum critical point and its associated Sachdev-Ye-Kitaev Planckian dynamics.

Constructive interference between disordered couplings enhances multiparty entanglement in quantum Heisenberg spin glass models

Disordered systems form one of the centrestages of research in many body sciences and lead to a plethora of interesting phenomena and applications. A paradigmatic disordered system consists of a one-dimensional array of quantum spin-1/2 particles, governed by the Heisenberg spin glass Hamiltonian with natural or engineered quenched disordered couplings in an external magnetic field. These systems allow disorder-induced enhancement for bipartite and multipartite observables. Here we show that simultaneous application of independent quenched disorders results in disorder-induced enhancement, while the same is absent with individual application of the same disorders. We term the phenomenon as constructive interference and the corresponding parameter stretches as the Venus regions. Interestingly, it has only been observed for multiparty entanglement and is absent for the single- and two-party physical quantities.

Low-temperature specific heat of some quantum mean-field glassy phases

We investigate analytically the low temperature behavior of the specific heat $C_v(T)$ for a large class of quantum disordered models within Mean Field approximation. This includes the vibrational modes of a lattice pinned by impurity disorder in the quantum regime, the quantum spherical $p$-spin-glass and a quantum Heisenberg spin glass. We exhibit a general mechanism, common to all these models, arising from the so-called marginality condition, responsible for the cancellation of the linear and quadratic contributions in $T$ in the specific heat. We thus find for all these models the Mean Field result $C_v(T) \propto T^3$.

Effects of anisotropy on a quantum Heisenberg spin glass on a three-dimensional hierarchical lattice

We study the anisotropic Heisenberg spin-glass model on a three-dimensional hierarchical lattice (designed to approximate the cubic lattice), within a real-space renormalization-group approach. Two different initial probability distributions for the exchange interaction (Jij), Gaussian and uniform, are used, with zero mean and width J. The (kT/J) x Delta0 phase diagram is obtained, where T is the temperature, Delta0 is the first moment of the probability distribution for the uniaxial anisotropy, and k is the Boltzmann constant. For the Ising model (Delta0 = 1), there is a spin-glass phase at low temperatures (high J) and a paramagnetic phase at high temperatures (low J). For the isotropic Heisenberg model (Delta0 = 0), our results indicate no spin-glass phase at finite temperatures. The transition temperature between the spin-glass and paramagnetic phase decreases with Delta0, as expected, but goes to zero at a finite value of the anisotropy parameter, namely Delta0 = Deltac approximately 0.59. Our results indicate that the whole transition line, between the paramagnetic and the spin-glass phases, for Deltac < Delta0 < 1, belongs to the same universality class as the transition for the Ising spin glass.

Dynamical solutions of a quantum Heisenberg spin glass model

We consider quantum-dynamical phenomena in the $\mathrm{SU}(2)$, $S=1/2$ infinite-range quantum Heisenberg spin glass. For a fermionic generalization of the model we formulate generic dynamical self-consistency equations. Using the Popov-Fedotov trick to eliminate contributions of the non-magnetic fermionic states we study in particular the isotropic model variant on the spin space. Two complementary approximation schemes are applied: one restricts the quantum spin dynamics to a manageable number of Matsubara frequencies while the other employs an expansion in terms of the dynamical local spin susceptibility. We accurately determine the critical temperature $T_c$ of the spin glass to paramagnet transition. We find that the dynamical correlations cause an increase of $T_c$ by 2% compared to the result obtained in the spin-static approximation. The specific heat $C(T)$ exhibits a pronounced cusp at $T_c$. Contradictory to other reports we do not observe a maximum in the $C(T)$-curve above $T_c$.

Spin glass versus superconductivity

A superconductor with interacting paramagnetic impurities is considered. The impurities are coupled via the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. At a temperature ${T}_{g},$ the system of magnetic impurities forms a spin-glass state. We study the effect of the spin-spin interactions on the superconducting transition point at $T&lt;{T}_{g}.$ We show that superconducting properties depend on the state of the spin system via spin-spin autocorrelation functions. With the help of the Keldysh technique, a general nonequilibrium Gor'kov equation is derived. Possible aging effects in the superconducting transition point are discussed. The equilibrium superconducting transition point is found explicitly and shown to be shifted towards higher temperatures and impurity concentrations compared to the classical Abrikosov-Gor'kov curve. The corresponding shift of the superconducting quantum critical point is quite small (about 10%). A method of calculating spin-spin correlation function is suggested. The method combines the ideas of random mean-field method and virial expansion. We calculate analytically the first virial term for the spin-spin correlator for the quantum Heisenberg spin glass with the RKKY interactions in the quasiequilibrium regime.

Out-of-equilibrium dynamics of a quantum Heisenberg spin glass

We study the out of equilibrium dynamics of the infinite range quantum Heisenberg spin glass model coupled to a thermal relaxation bath. The SU(2) spin algebra is generalized to SU(N) and we analyse the large-N limit. The model displays a dynamical phase transition between a paramagnetic and a glassy phase. In the latter, the system remains out of equilibrium and displays an aging phenomenon, which we characterize using both analytical and numerical methods. In the aging regime, the quantum fluctuation-dissipation relation is violated and replaced at very long time by its classical generalization, as in models involving simple spin algebras studied previously. We also discuss the effect of a finite coupling to the relaxation baths and their possible forms. This work completes and justifies previous studies on this model using a static approach.

Fermionic Heisenberg glasses with BCS pairing interaction

We have analyzed a fermionic infinite-ranged quantum Heisenberg spin glass with BCS coupling in real space in the presence of a magnetic field. It has been possible to locate the transition line between the normal–paramagnetic phase and the phase where there is a long-range order corresponding to pair formation in sites. The nature of the transition line is also investigated. This transition ends at T f, the transition temperature between NP and spin glass phase where the static approximation and replica symmetry ansatz are reliable.

Fermionic Heisenberg model for spin glasses with BCS pairing interaction

In the present paper we have analysed a fermionic infinite-ranged quantum Heisenberg spin glass (s=1/2) with a BCS coupling in real space in the presence of an applied magnetic field. This model has been obtained by tracing out the conducting fermions in a superconducting alloy. The magnetic field is applied in the resulting effective model. The problem is formulated in the path integral formalism where the spin variables are defined as bilinear combinations of the Grassmann fields. The static approximation is used to treat both the pairing and the spin terms together with the replica symmetry ansatz. Henceforth, the problem can be reduced to a one site problem. The field in the z direction, Hz, separates the order parameters in two groups: parallel and transverse to it. We have obtained a phase diagram in T-g space with zero transverse spin-glass ordering, g being the strength of the pairing interaction. It has been possible to locate the transition temperature between the normal paramagnetic phase (NP) and the phase where there is a long range order corresponding to formation of pairs (PAIR). The transition ends at the temperature Tf, the transition temperature between the NP phase and the spin glass (SG) phase. Tf decreases for stronger fields allowing us to calculate the NP-PAIR line transition even at low temperatures. The NP-PAIR transition line has a complex dependence with g and Hz, having a tricritical point depending on Hz from where second order transitions occur for higher values of g and first order transitions occur for lower values of g.

Static thermodynamic quantities of quantum Heisenberg spin glasses with anisotropic interaction in applied magnetic fields.

In the static replica symmetric approximation, the quantum Heisenberg spin-glass model with the infinite-ranged random Dzyaloshinskii-Moriya interaction in external magnetic fields is investigated in detail. The local susceptibility and the corresponding order parameters are calculated, which are in good agreement with those of thermofield calculations. The dependencies of entropy and specific heat on temperature are studied numerically at various magnetic fields and for different spin numbers. It is shown that the entropy is always positive and the quantum fluctuation has very strong effect on specific heat. Our results show that the typical specific heat of a spin glass for different magnetic fields exhibits crossover behavior, which has been obtained experimentally but not explained theoretically before.

Specific Heat of Quantum Heisenberg Spin Glasses: Magnetic Field Effects

The quantum spin glass theory with the infinite-range random Dzyaloshinskii-Moriya interaction presented by Yi and his cooperators is investigated numerically at a fixed anisotropy interaction for different external magnetic fields and spin number 1/2. Specifically, the dependences of the typical specific heat and entropy of spin glass on temperatures have been obtained theoretically.

Correlations in vector-spin-glass models in a transverse field.

Several publications dealing with the infinite-range quantum XY and Heisenberg spin glasses in an external magnetic field K in the z direction share a common supposition: the correlation between the x and y components of the spins is zero. Using the Matsubara imaginary-time formalism we show that this assumption holds only for those models where K=0. With the help of the Trotter-Suzuki formulation we investigate the phase diagram of the XY model for spin S=1/2, and find that it is different from those previously reported because of the nonzero xy correlation. It is also argued that for a general spin S in the XY model at zero temperature the spin-glass phase persists up to ${\mathit{K}}_{\mathit{c}}$=2S.

Field theoretic derivation and extension of Sherrington-Kirkpatrick and Parisi spin glass solutions

Applying a new decoupling scheme we derive SK and Parisi solutions for Ising and quantum Heisenberg spin glass models with Grassmann representations of spins. For a metallic spin glass model we find a linear decrease of the spin glass critical temperature with the elastic scattering time of electrons.

Field-induced crossover behavior in quantum Heisenberg spin glasses with random-anisotropy axes.

The infinite-range quantum Heisenberg spin-glass model with random-anisotropy axes and external magnetic field (h) is studied by means of the thermofield dynamics for the spin value S=1/2. The stability of the mean-field-type solution against the action of fluctuations has been evaluated in the presence of h leading to the upper and lower critical lines in the field-temperature (h-T) plane. For small values of the anisotropy variance we find a crossover of the upper critical line from the de Almeida--Thouless-type behavior for small fields to the Gabay-Toulouse-like behavior for large fields and a reversed type of behavior at the lower critical line for corresponding values of the random anisotropy---in close analogy to the recently analyzed quantum vector spin glass with random Dzyaloshinsky-Moriya interactions.

Quantum vector spin-glass in a field: results for general spin

In this paper we investigate the infinite-ranged quantum Heisenberg spin-glass in an applied field for a general spin s without the use of the static approximation. The Suzuki-Trotter method is used to map the system into a classical one for general spin s. Results for spin 1 2 and spin 1 are explicitly obtained and the phase diagram agrees qualitatively but not exactly with previous results obtained by us using the static approximation.

Quantum HeisenbergS=1 spin glass: Effect of anisotropy and ferromagnetic interaction

A theoretical analysis is given for the phase structure of the infinite-range quantum Heisenberg spin glass with uniaxial anisotropy (D) and coaxial external magnetic field (h) in the presence of ferromagnetic interaction. The thermofield dynamics is used as a substitute for then-replica trick, including a generalisation of the de Almeida-Thouless stability analysis. Within a mean-field theory a multiplicity of spin glass phases has been found for the spin valueS=1, including: longitudinal, transverse and mixed spin glass phases. Additionally, phases with long range order turn out to exist: collinear and randomly canted ferromagnetic states (ferromagnet and spin glass). Phase transition points and lines are found in the temperature-field plane for various values of the ferromagnetic coupling (J 0) together with irreversibility crossovers.

Quantum vector spin-glass models in an applied field

We use the static approximation to investigate the phase diagram of the infinite-ranged quantum Heisenberg spin glass (QHSG) in an external field, as well as the phase diagram of a two-component quantum spin glass (QXYSG) in a transverse or a longitudinal field. For the QHSG we find that, for strong field (H) and low temperature (T), the phase transition into the spin-glass phase characterized by nonzero transverse spin-glass ordering is given by ${\mathit{T}}_{\mathit{c}}$\ensuremath{\sim}exp[-${\mathit{H}}^{2}$/(2${\mathit{J}}^{2}$${\mathit{S}}^{2}$)], as compared with ${\mathit{T}}_{\mathit{c}}$\ensuremath{\sim}exp{-${\mathit{H}}^{2}$/[2${\mathit{J}}^{2}$S(S+1)]} for classical spins of magnitude \ensuremath{\surd}S(S+1) . In the case of QXYSG in a transverse field (\ensuremath{\Gamma}), the phase boundary terminates at \ensuremath{\Gamma}/J=2 for T=0.