Spin Chain Model Research Articles

Ground-state-entanglement bound for quantum energy teleportation of general spin-chain models

Many-body quantum systems in the ground states have zero-point energy due to the uncertainty relation. In many cases, the system in the ground state accompanies spatially-entangled energy density fluctuation via the noncommutativity of the energy density operators, though the total energy takes a fixed value, i.e. the lowest eigenvalue of the Hamiltonian. Quantum energy teleportation (QET) is protocols for extraction of the zero-point energy out of one subsystem using information of a remote measurement of another subsystem. From an operational viewpoint of protocol users, QET can be regarded as an effective rapid energy transportation without breaking all physical laws including causality and local energy conservation. In the protocols, the ground-state entanglement plays a crucial role. In this paper, we show analytically for a general class of spin-chain systems that the entanglement entropy is lower bounded by a positive quadratic function of the teleported energy between the regions of a QET protocol. This supports a general conjecture that ground-state entanglement is an evident physical resource for energy transportation in the context of QET. The result may also deepen our understanding of the energy density fluctuation in condensed matter systems from a new perspective of quantum information theory.

The Diagonalization of Hamiltonian in XY Spin Chain with Dzyaloshinskii–Moriya and Three-Body Interactions

By the methods of Jordan–Wigner transformation and Bogolyubov transformation, in this paper, we diagonalized the Hamiltonian in one-dimensional Heisenberg spin chain model with Dzyaloshinskii–Moriya interactions and three-body interactions, and further analyze the effect of the Dzyaloshinskii–Moriya interaction and different three-body interactions on the Bogolyubov transformation and the energy spectrum of quantum spin chains. The results shows that only the energy spectrum but not the coefficients of the Bogolyubov transformation depends on DM interaction and one type of three-site exchange interaction. Another kind of three-body interaction not only can move the criticality region, but also can generate a new critical point.

Structure and magnetism of Cr2[BP3O12]: Towards the quantum-classical crossover in a spin-32alternating chain

Magnetic properties of the spin-3/2 Heisenberg system Cr2BP3O12 are investigated by magnetic susceptibility chi(T) measurements, electron spin resonance, neutron diffraction, and density functional theory (DFT) calculations, as well as classical and quantum Monte Carlo (MC) simulations. The broad maximum of chi(T) at 85K and the antiferromagnetic Weiss temperature of 139 K indicate low-dimensional magnetic behavior. Below TN = 28 K, Cr2BP3O12 is antiferromagnetically ordered with the k = 0 propagation vector and an ordered moment of 2.5 muB/Cr. DFT calculations, including DFT+U and hybrid functionals, yield a microscopic model of spin chains with alternating nearest-neighbor couplings J1 and J1' . The chains are coupled by two inequivalent interchain exchanges of similar strength (~1-2 K), but different sign (antiferromagnetic and ferromagnetic). The resulting spin lattice is quasi-one-dimensional and not frustrated. Quantum MC simulations show excellent agreement with the experimental data for the parameters J1 ~= 50 K and J1'/J1 ~= 0.5. Therefore, Cr2BP3O12 is close to the gapless critical point (J1'/J1 = 0.41) of the spin-3/2 bond-alternating Heisenberg chain. The applicability limits of the classical approximation are addressed by quantum and classical MC simulations. Implications for a wide range of low-dimensional S = 3/2 materials are discussed.

Crystal structures and variable magnetism of PbCu2(XO3)2Cl2 with X = Se, Te

Novel Cu(2+)-based compounds PbCu2(SeO3)2Cl2 (space group C2/c; a = 13.056(1) Å; b = 9.5567(9) Å; c = 6.9006(6) Å; β = 90.529(7)°; RI = 0.0371) and PbCu2(TeO3)2Cl2 (space group P2(1); a = 7.2401(2) Å; b = 7.2688(2) Å; c = 8.2846(2) Å; β = 96.416(2)°; R(I) = 0.0570) have been obtained by solid-state synthesis. Their crystal structures are remarkably dissimilar and underlie a very different magnetic behavior. While PbCu2(SeO3)2Cl2 can be well described by a spin-chain model with an exchange coupling of J1 ≃ 160 K, PbCu2(TeO3)2Cl2 is a spin-dimer system that, however, features a comparable magnetic nearest-neighbor coupling of J ≃ 213 K. PbCu2(SeO3)2Cl2 orders antiferromagnetically below 12 K, whereas PbCu2(TeO3)2Cl2 lacks long-range magnetic order down to at least 2 K, owing to the strong dimerization of the Cu(2+) spins. Crystal structures of both compounds are rationalized in terms of relevant magnetic exchange pathways, and the implications for a broader range of Cu(2+) compounds are discussed.

Spin chains and Arnold's problem on the Gauss-Kuz'min statistics for quadratic irrationals

New results related to number theoretic model of spin chains are proved. We solve Arnold's problem on the Gauss-Kuz'min statistics for quadratic irrationals.Bibliography: 24 titles.

Quantum corrections to ϕ 4 model solutions and applications to Heisenberg chain dynamics

AbstractThe Heisenberg spin chain is considered in ϕ 4 model approximation. Quantum corrections to classical solutions of the one-dimensional ϕ 4 model within the correspondent physics are evaluated with account of rest d-1 dimensions of a d-dimensional theory. A quantization of the model is considered in terms of spacetime functional integral. The generalized zeta-function formalism is used to renormalize and evaluate the functional integral and quantum corrections to energy in a quasiclassical approximation. The results are applied to appropriate conditions of the spin chain model and its dynamics, for which elementary solutions, energy and the quantum corrections are calculated.

An Approach to Loop Quantum Cosmology Through Integrable Discrete Heisenberg Spin Chains

The quantum evolution equation of Loop Quantum Cosmology (LQC) -- the quantum Hamiltonian constraint -- is a difference equation. We relate the LQC constraint equation in vacuum Bianchi I separable (locally rotationally symmetric) models with an integrable differential-difference nonlinear Schr\"odinger type equation, which in turn is known to be associated with integrable, discrete Heisenberg spin chain models in condensed matter physics. We illustrate the similarity between both systems with a simple constraint in the linear regime.

Ferrimagnetic spin-1/2 chain of alternating Ising and Heisenberg spins in arbitrarily oriented magnetic field

The ferrimagnetic spin-1/2 chain composed of alternating Ising and Heisenberg spins in an arbitrarily oriented magnetic field is exactly solved using the spin-rotation transformation and the transfer-matrix method. It is shown that the low-temperature magnetization process depends basically on a spatial orientation of the magnetic field. A sharp stepwise magnetization curve with a marked intermediate plateau, which emerges for the magnetic field applied along the easy-axis direction of the Ising spins, becomes smoother and the intermediate plateau shrinks if the external field is tilted from the easy-axis direction. The magnetization curve of a polycrystalline system is also calculated by performing powder averaging of the derived magnetization formula. The proposed spin-chain model brings an insight into high-field magnetization data of 3d-4f bimetallic polymeric compound Dy(NO_3)(DMSO)_2Cu(opba)(DMSO)_2, which provides an interesting experimental realization of the ferrimagnetic chain composed of two different but regularly alternating spin-1/2 magnetic ions Dy^{3+} and Cu^{2+} that are reasonably approximated by the notion of Ising and Heisenberg spins, respectively.

Nonperturbative dynamical decoupling control: A spin-chain model

This paper considers a spin-chain model by numerically solving the exact model to explore the nonperturbative dynamical decoupling regime, where an important issue recently arose. Our study has revealed a few universal features of nonperturbative dynamical control irrespective of the types of environments and system-environment couplings. We have shown that, for the spin-chain model, there is a threshold and a large pulse parameter region where the effective dynamical control can be implemented, in contrast to the perturbative decoupling schemes where the permissible parameters are represented by a point or converge to a very small subset in the large parameter region admitted by our nonperturbative approach. An important implication of the nonperturbative approach is its flexibility in implementing the dynamical control scheme in an experimental setup. Our findings have exhibited several interesting features of the nonperturbative regimes such as the chain-size independence, pulse strength upper bound, noncontinuous valid parameter regions, etc. Furthermore, we find that our nonperturbative scheme is robust against randomness in model fabrication and time-dependent random noise.

Dynamical role of system-environment correlations in non-Markovian dynamics

We analyse the role played by system-environment correlations in the emergence of non-Markovian dynamics. By working within the framework developed in Breuer et al., Phys. Rev. Lett. 103, 210401 (2009), we unveil a fundamental connection between non-Markovian behaviour and dynamics of system-environment correlations. We derive an upper bound to the rate of change of the distinguishability between different states of the system that explicitly depends on the development and establishment of correlations between system and environment. We illustrate our results using a fully solvable spin-chain model, which allows us to gain insight on the mechanisms triggering non-Markovian evolution.

Quantum phase transitions in the exactly solved spin-1/2 Heisenberg–Ising ladder

The ground-state behaviour of the frustrated quantum spin-1/2 two-leg ladder with the Heisenberg intra-rung and Ising inter-rung interactions is examined in detail. The investigated model is transformed into the quantum Ising chain with composite spins in an effective transverse and longitudinal field by employing either the bond-state representation or the unitary transformation. It is shown that the ground state of the Heisenberg–Ising ladder can be descended from three exactly solvable models: the quantum Ising chain in a transverse field, the ‘classical’ Ising chain in a longitudinal field or the spin-chain model in a staggered longitudinal–transverse field. The last model serves in evidence of the staggered bond phase with alternating singlet and triplet bonds on the rungs of a two-leg ladder, which appears at moderate values of the external magnetic field and consequently leads to a fractional plateau at a half of the saturation magnetization. The ground-state phase diagram totally consists of five ordered and one quantum paramagnetic phase, which are separated from each other either by the lines of discontinuous or continuous quantum phase transitions. The order parameters are exactly calculated for all five ordered phases and the quantum paramagnetic phase is characterized through different short-range spin–spin correlations.

Holographic entanglement entropy in Suzuki-Trotter decomposition of spin systems

In quantum spin chains at criticality, two types of scaling for the entanglement entropy exist: one comes from conformal field theory (CFT), and the other is for entanglement support of matrix product state (MPS) approximation. On the other hand, the quantum spin-chain models can be mapped onto two-dimensional (2D) classical ones by the Suzuki-Trotter decomposition. Motivated by the scaling and the mapping, we introduce information entropy for 2D classical spin configurations as well as a spectrum, and examine their basic properties in the Ising and the three-state Potts models on the square lattice. They are defined by the singular values of the reduced density matrix for a Monte Carlo snapshot. We find scaling relations of the entropy compatible with the CFT and the MPS results. Thus, we propose that the entropy is a kind of "holographic" entanglement entropy. At T(c), the spin configuration is fractal, and various sizes of ordered clusters coexist. Then, the singular values automatically decompose the original snapshot into a set of images with different length scales, respectively. This is the origin of the scaling. In contrast to the MPS scaling, long-range spin correlation can be described by only few singular values. Furthermore, the spectrum, which is a set of logarithms of the singular values, also seems to be a holographic entanglement spectrum. We find multiple gaps in the spectrum, and in contrast to the topological phases, the low-lying levels below the gap represent spontaneous symmetry breaking. These contrasts are strong evidence of the dual nature of the holography. Based on these observations, we discuss the amount of information contained in one snapshot.

Theory of quantum energy transfer in spin chains: Superexchange and ballistic motion

Quantum energy transfer in a chain of two-level (spin) units, connected at its ends to two thermal reservoirs, is analyzed in two limits: (i) in the off-resonance regime, when the characteristic subsystem excitation energy gaps are larger than the reservoirs frequencies, or the baths temperatures are low and (ii) in the resonance regime, when the chain excitation gaps match populated bath modes. In the latter case, the model is studied using a master equation approach, showing that the dynamics is ballistic for the particular chain model explored. In the former case, we analytically study the system dynamics utilizing the recently developed Energy-Transfer Born-Oppenheimer formalism [L.-A. Wu and D. Segal, Phys. Rev. E 83, 051114 (2011)], demonstrating that energy transfers across the chain in a superexchange (bridge assisted tunneling) mechanism, with the energy current decreasing exponentially with distance. This behavior is insensitive to the chain details. Since at low temperatures the excitation spectrum of molecular systems can be truncated to resemble a spin chain model, we argue that the superexchange behavior obtained here should be observed in widespread systems satisfying the off-resonance condition.

Symmetry-protected topological orders of one-dimensional spin systems withD2+Tsymmetry

In Liu et al. [Phys. Rev. B 84, 075135 (2011)] we studied eight gapped symmetric quantum phases in $S=1$ spin chains/ladders which respect a discrete spin rotation ${D}_{2}\ensuremath{\subset}SO(3)$ and time reversal $T$ symmetries. In this paper, using a generalized approach, we study all the 16 possible gapped symmetric quantum phases of one-dimensional (1D) integer spin systems with ${D}_{2}+T$ symmetry. Those phases are beyond Landau symmetry breaking theory and cannot be characterized by local order parameters since they do not break any symmetry. They correspond to 16 symmetry protected topological (SPT) orders. We show that all the 16 SPT orders can be fully characterized by the physical properties of the symmetry protected degenerate boundary states at the ends of a chain segment. So we can measure and distinguish all the 16 SPT orders experimentally. We also show that all these SPT orders can be realized in $S=1$ spin chain or spin ladder models. The gapped symmetric phases protected by subgroups of ${D}_{2}+T$ are also studied. Again, all these phases can be distinguished by physically measuring their end ``spins.''

Dynamics of azurite Cu3(CO3)2(OH)2in a magnetic field as determined by neutron scattering

Azurite, a natural mineral made up of CuO chains, is also an intriguing spin-1/2 quantum magnet. There has been much debate as to the 1-dimensional (1D) nature of this material by theorists and experimentalists alike. The focus of this debate lies in the interactions between Cu-ions within the antiferromagnetically ordered state below 1.9 K. We present high-resolution inelastic neutron scattering data which highlight the complexity of the magnetic ground state of azurite. The application of magnetic fields and temperatures were used to probe the excitations revealing important information about the dynamics in this system. From this we are able to conclude that the 1D Heisenberg antiferromagnetic spin chain model is not sufficient to describe the dynamics in azurite. Instead additional coupling including interchain interactions and an anisotropic staggered field are necessary to fully model the observed excitations.

Baxter’sT-Q equation, SU(N)/SU(2) N − 3 correspondence and Ω-deformed Seiberg-Witten prepotential

We study Baxter's T-Q equation of XXX spin-chain models under the semiclassical limit where an intriguing SU(N)/SU(2)^{N-3} correspondence emerges. That is, two kinds of 4D \mathcal{N}=2 superconformal field theories having the above different gauge groups are encoded simultaneously in one Baxter's T-Q equation which captures their spectral curves. For example, while one is SU(N_c) with N_f=2N_c flavors the other turns out to be SU(2)^{N_c-3} with N_c hyper-multiplets (N_c > 3). It is seen that the corresponding Seiberg-Witten differential supports our proposal.

Dislocation-mediated melting of one-dimensional Rydberg crystals

We consider cold Rydberg atoms in a one-dimensional optical lattice in the Mott regime with a single atom per site at zero temperature. An external laser drive with Rabi frequency $\ensuremath{\Omega}$ and laser detuning $\ensuremath{\Delta}$ creates Rydberg excitations whose dynamics is governed by an effective spin-chain model with (quasi) long-range interactions. This system possesses intrinsically a large degree of frustration resulting in a ground-state phase diagram in the $(\ensuremath{\Delta},\ensuremath{\Omega})$ plane with a rich topology. As a function of $\ensuremath{\Delta}$, the Rydberg blockade effect gives rise to a series of crystalline phases commensurate with the optical lattice that form a so-called devil's staircase. The Rabi frequency $\ensuremath{\Omega}$, on the other hand, creates quantum fluctuations that eventually lead to a quantum melting of the crystalline states. Upon increasing $\ensuremath{\Omega}$, we find that generically a commensurate-incommensurate transition to a floating Rydberg crystal that supports gapless phonon excitations occurs first. For even larger $\ensuremath{\Omega}$, dislocations within the floating Rydberg crystal start to proliferate and a second, Kosterlitz-Thouless-Nelson-Halperin-Young dislocation-mediated melting transition finally destroys the crystalline arrangement of Rydberg excitations. This latter melting transition is generic for one-dimensional Rydberg crystals and persists even in the absence of an optical lattice. The floating phase and the concomitant transitions can, in principle, be detected by Bragg scattering of light.

Frustrated couplings between alternating spin-12chains in AgVOAsO4

We report on the crystal structure and magnetic behavior of the spin-1/2 compound AgVOAsO4. Magnetic susceptibility, high-field magnetization, and electron spin resonance measurements identify AgVOAsO4 as a gapped quantum magnet with a spin gap Delta ~ 13 K and a saturation field H_s ~ 48.5 T. Extensive band structure calculations establish the microscopic magnetic model of spin chains with alternating exchange couplings J ~ 40 K and J' ~ 26 K. However, the precise evaluation of the spin gap emphasizes the role of interchain couplings which are frustrated due to the peculiar crystal structure of the compound. The unusual spin model and the low energy scale of the exchange couplings make AgVOAsO4 a promising candidate for an experimental investigation of Bose-Einstein condensation and other exotic ground states in high magnetic fields.

Noncompact sl(N) Spin Chains: BGG-Resolution, Q-Operators and Alternating Sum Representation for Finite-Dimensional Transfer Matrices

We study properties of transfer matrices in the sl(N) spin chain models. The transfer matrices with an infinite-dimensional auxiliary space are factorized into the product of N commuting Baxter $${\mathcal{Q}}$$ -operators. We consider the transfer matrices with auxiliary spaces of a special type (including the finite-dimensional ones). It is shown that they can be represented as the alternating sum over the transfer matrices with infinite- dimensional auxiliary spaces. We show that certain combinations of the Baxter $${\mathcal{Q}}$$ -operators can be identified with the Q-functions, which appear in the Nested Bethe Ansatz.

Exploiting Kondo spin chains for generating long range distance independent entanglement

We investigate the entanglement properties of the Kondo spin chain when it is prepared in its ground state as well as its dynamics following a single bond quench. We show that a true measure of entanglement such as negativity enables to characterize the unique features of the gapless Kondo regime. We determine the spatial extent of the Kondo screening cloud and propose an ansatz for the ground state in the Kondo regime accessible to this spin chain; we also demonstrate that the impurity spin is indeed maximally entangled with the Kondo cloud. We exploit these features of the entanglement in the gapless Kondo regime to show that a single local quench at one end of a Kondo spin chain may always induce a fast and long lived oscillatory dynamics, which establishes a high quality entanglement between the individual spins at the opposite ends of the chain. This entanglement is a footprint of the presence of the Kondo cloud and may be engineered so as to attain--even for very large chains--a constant high value independent of the length; in addition, it is thermally robust. Moreover, we show that high entanglement between very distant boundary spins is generated by suddenly connecting two long Kondo spin chains. We show that this procedure provides an efficient way to route entanglement between multiple distant sites. To better evidence the remarkable peculiarities of the Kondo regime, we carry a parallel analysis of the entanglement properties of the Kondo spin chain model in the gapped dimerised regime where these remarkable features are absent.