XXZ Heisenberg Model Research Articles

Topological invariant and cotranslational symmetry in strongly interacting multi-magnon systems

It is still an outstanding challenge to characterize and understand the topological features of strongly interacting states such as bound states in interacting quantum systems. Here, by introducing a cotranslational symmetry in an interacting multi-particle quantum system, we systematically develop a method to define a Chern invariant, which is a generalization of the well-known Thouless–Kohmoto–Nightingale–den Nijs invariant, for identifying strongly interacting topological states. As an example, we study the topological multi-magnon states in a generalized Heisenberg XXZ model, which can be realized by the currently available experiment techniques of cold atoms (Aidelsburger et al 2013 Phys. Rev. Lett. 111, 185301; Miyake et al 2013 Phys. Rev. Lett. 111, 185302). Through calculating the two-magnon excitation spectrum and the defined Chern number, we explore the emergence of topological edge bound states and give their topological phase diagram. We also analytically derive an effective single-particle Hofstadter superlattice model for a better understanding of the topological bound states. Our results not only provide a new approach to defining a topological invariant for interacting multi-particle systems, but also give insights into the characterization and understanding of strongly interacting topological states.

Quantum Otto heat engine with three-qubit [formula omitted] model as working substance

A quantum Otto heat engine is established with a three-qubit Heisenberg XXZ model with Dzyaloshinskii–Moriya (DM) interaction under a homogeneous magnetic field as the working substance. The quantum Otto engine is composed of two quantum isochoric processes and two quantum adiabatic processes. Here we have restricted Bc∕Bh=Jc∕Jh=r in the two adiabatic processes, where r is the adiabatic compression ratio. The work output and efficiency are calculated for our cycle. The possible adiabatic compression ratios and the ratios of work output between our working substance and a single spin under the same external conditions in the Otto cycle are analyzed with different DM interaction parameters and anisotropic parameters. The effects of pairwise entanglements on the heat engine efficiency are discussed.

A TBA approach to thermal transport in the XXZ Heisenberg model

We show that the thermal Drude weight and magnetothermal coefficient of the 1D easy-plane Heisenberg model can be evaluated by an extension of the Bethe ansatz thermodynamics formulation by Takahashi and Suzuki (1972 Prog. Theor. Phys. 48 2187). They have earlier been obtained by the quantum transfer matrix method (Klümper 1999 Z. Phys. B 91 507). Furthermore, this approach can be applied to the study of the far-out of equilibrium energy current generated at the interface between two semi-infinite chains held at different temperatures.

Nonlinear field space cosmology

We consider the FRW cosmological model in which the matter content of universe (playing a role of inflaton or quintessence) is given by a novel generalization of the massive scalar field. The latter is a scalar version of the recently introduced Nonlinear Field Space Theory (NFST), where physical phase space of a given field is assumed to be compactified at large energies. For our analysis we choose the simple case of a field with the spherical phase space and endow it with the generalized Hamiltonian analogous to the XXZ Heisenberg model, normally describing a system of spins in condensed matter physics. Subsequently, we study both the homogenous cosmological sector and linear perturbations of such a test field. In the homogenous sector we find that nonlinearity of the field phase space is becoming relevant for large volumes of universe and then it can lead to a recollapse, and possibly also at very high energies, leading to the phase of a bounce. Quantization of the field is performed in the limit where nontrivial nature of its phase space can be neglected, while there is a non-vanishing contribution from the Lorentz symmetry breaking term of the Hamiltonian. As a result, in the leading order of the XXZ anisotropy parameter, we find that the inflationary spectral index remains unmodified with respect to the standard case but the total amplitude of perturbations is subject to a correction. The Bunch-Davies vacuum state also becomes appropriately corrected. The proposed new approach is bringing cosmology and condensed matter physics closer together, which may turn out to be beneficial for both disciplines.

Various quantum measures and quantum phase transition within one-dimensional anisotropic spin-1/2 Heisenberg XXZ model

In this work, we investigate the dynamical properties of various quantum measures (quantum coherence and correlations) to estimate the system evolution under spin-1/2 Heisenberg XXZ model by utilizing quantum renormalization-group method. It has been shown that quantum coherence and correlations can be used to effectively detect a quantum critical point associated with a quantum phase transition (QPT) after several iterations of renormalization. Additionally, we obtain that the dynamical behavior of l1 norm of coherence is in agreement with that of concurrence and double trace distance discord. Interestingly, Bell-CHSH inequality cannot be violated with increasing of the spin system size N. That is, the block-block Bell nonlocality cannot be revealed. Moreover, we reveal some quantitative relations between quantum coherence and some quantum correlations, and thus the l1 norm of coherence is more conducive for probing the QPT at the critical point within the composite systems. Further, the scaling behaviors and nonanalytic phenomenon of the l1 norm of coherence and quantum discord are discussed in detail.

Quantum entanglement and critical exponents in one-dimensional spin-1 bond-alternating XXZ chains

The characterization of the quantum phase transition in a lowdimensional system has attracted a considerable amount of attention in quantum manybody systems. As one of the fundamental models in quantum magnetism, spin-1 models have richer phase diagrams and show more complex physical phenomena. In the spin-1 antiferromagnetic XXZ model, the Haldane phase and the Nel phase are the gapped topologic phases which cannot be characterized by the local order parameters. To characterize the nature in such phases, one has to calculate the non-local long range order parameters. Normally, the non-local order parameter in the topological phase is obtained from the extrapolation of finite-sized system in numerical study. However, it is difficult to extract the critical exponents with such an extrapolated non-local order parameter due to the numerical accuracy. In a recently developed tensor network representation, i.e., the infinite matrix product state (iMPS) algorithm, it was shown that the non-local order can be directly calculated from a very large lattice distance in an infinite-sized system rather than an extrapolated order parameter in a finite-sized system. Therefore, it is worthwhile using this convenient technique to study the non-local orders in the topological phases and characterize the quantum criticalities in the topological quantum phase transitions. In this paper, by utilizing the infinite matrix product state algorithm based on the tensor network representation and infinite time evolving block decimation method, the quantum entanglement, fidelity, and critical exponents of the topological phase transition are investigated in the one-dimensional infinite spin-1 bond-alternating XXZ Heisenberg model. It is found that there is always a local dimerization order existing in the whole parameter range when the bond-alternative strength parameter changes from 0 to 1. Also, due to the effect of the bond-alternating, there appears a quantum phase transition from the long-rang ordering topological Nel phase to the local ordering dimerization phase. The von Neumann entropy, fidelity per lattice site, and order parameters all give the same phase transition point at c = 0.638. To identify the type of quantum phase transition, the central charge c 0.5 is extracted from the ground state von Neumann entropy and the finite correlation length, which indicates that the phase transition belongs to the two-dimensional Ising universality class. Furthermore, it is found that the Nel order and the susceptibility of Nel order have power-law relations to |-c|. From the numerical fitting of the Nel order and its susceptibility, we obtain the characteristic critical exponents ' = 0.236 and ' = 0.838. It indicates that such critical exponents from our method characterize the nature of the quantum phase transition. Our critical exponents from the iMPS method can provide guidance for studying the properties of the phase transition in quantum spin systems.

Topological Basis Method for Four-Qubit Spin- 1 2 $\frac {1}{2}$ XXZ Heisenberg Chain with Dzyaloshinskii-Moriya Interaction

In this paper, we investigate the four-qubit spin-\(\frac {1}{2}\) XXZ Heisenberg chain with Dzyaloshinskii-Moriya interaction by topological basis method, and research the relationship between the topological basis states and the ground states. In order to study the Hamiltonian system beyond XXZ model, we introduce two Temperley-Lieb algebra generators and two other generalized generators. Then we investigate the relationship between topological basis and Heisenberg XXZ model with Dzyaloshinskii-Moriya interaction. The results show that the ground state of this model falls on the topological basis state for anti-ferromagnetic case and gapless phase case.

Nonperturbative linked-cluster expansions in long-range ordered quantum systems

We introduce a generic scheme to perform non-perturbative linked cluster expansions in long-range ordered quantum phases. Clusters are considered to be surrounded by an ordered reference state leading to effective edge-fields in the exact diagonalization on clusters which break the associated symmetry of the ordered phase. Two approaches, based either on a self-consistent solution of the order parameter or on minimal sensitivity with respect to the ground-state energy per site, are formulated to find the optimal edge-field in each NLCE order. Furthermore, we investigate the scaling behavior of the NLCE data sequences towards the infinite-order limit. We apply our scheme to gapped and gapless ordered phases of XXZ Heisenberg models on various lattices and for spins 1/2 and 1 using several types of cluster expansions ranging from a full-graph decomposition, rectangular clusters, up to more symmetric square clusters. It is found that the inclusion of edge-fields allows to regularize non-perturbative linked-cluster expansions in ordered phases yielding convergent data sequences. This includes the long-range spin-ordered ground state of the spin-1/2 and spin-1 Heisenberg model on the square and triangular lattice as well as the trimerized valence bond crystal of the spin-1 Heisenberg model on the kagome lattice.

Renormalization of quantum deficit and monogamy relation in the Heisenberg XXZ model

In this study, the dynamical behavior of quantum deficit and monogamy relation in the Heisenberg XXZ model is investigated by implementing quantum renormalization group theory. The results demonstrate that the quantum deficit can be used to capture the quantum phase transitions point and show scaling behavior with the spin chain size increasing. It was also found that the critical exponent has no change when varying measure from entanglement to quantum correlation. The monogamy relation is influenced by the steps of quantum renormalization group and the ways of splitting the block states. Furthermore, the monogamy relation of generalized W state also is given by means of quantum deficit.

Distribution of Quantum Coherence in Multipartite Systems.

The distribution of coherence in multipartite systems is examined. We use a new coherence measure with entropic nature and metric properties, based on the quantum Jensen-Shannon divergence. The metric property allows for the coherence to be decomposed into various contributions, which arise from local and intrinsic coherences. We find that there are trade-off relations between the various contributions of coherence, as a function of parameters of the quantum state. In bipartite systems the coherence resides on individual sites or is distributed among the sites, which contribute in a complementary way. In more complex systems, the characteristics of the coherence can display more subtle changes with respect to the parameters of the quantum state. In the case of the XXZ Heisenberg model, the coherence changes from a monogamous to a polygamous nature. This allows us to define the shareability of coherence, leading to monogamy relations for coherence.

Вплив анізотропії обмінної взаємодії Гайзенберга на процес намагнічення фрустрованого ромбічного ланцюжка у сильному магнітному полі

A frustrated diamond spin chain in a z- or x-aligned external magnetic field has been considered in the framework of the spin-1/2 antiferromagnetic XXZ Heisenberg model. The magnetization process of the frustrated diamond spin chain is analyzed, by using the effective models found in the strong-coupling approximation in the case where the Heisenberg interaction anisotropy parameter Δ > 1. The theory is applied to explain experimental data for natural mineral azurite, Cu3(CO3)2(OH)2.

Renormalization of the global quantum correlation and monogamy relation in the anisotropic Heisenberg XXZ model

In this study, the global quantum correlation, monogamy relation and quantum phase transition of the Heisenberg XXZ model are investigated by the method of quantum renormalization group. We obtain, analytically, the expressions of the global negativity, the global measurement-induced disturbance and the monogamy relation for the system. The result shows that for a three-site block state, the partial transpose of an asymmetric block can get stronger entanglement than that of the symmetric one. The residual entanglement and the difference of the monogamy relation of measurement-induced disturbance show a scaling behavior with the size of the system becoming large. Moreover, the monogamy nature of entanglement measured by negativity exists in the model, while the nonclassical correlation quantified by measurement-induced disturbance violates the monogamy relation and demonstrates polygamy.

Effect of Dzyaloshinskii-Moriya Interaction on Thermal Quantum Correlation in a Two-Qubit Heisenberg XXZ Model with an Inhomogeneous External Magnetic Field

By using the two-qubit Heisenberg XXZ model with Dzyaloshinskii-Moriya (DM) interaction and an inhomogeneous external magnetic field, we investigate the similarities and differences of negativity (N), quantum discord (QD), and measurement-induced disturbance (MID) and the behaviors of quantum phase transition (QPT) at finite temperature. The results indicate that DM interaction D can enhance the N, QD, and MID, while the uniform magnetic field B suppresses them, and the role played by the inhomogeneity b of magnetic field in N is obviously different from those in QD and MID for the smaller D region. Moreover, compared with N, we notice the QD and MID are more general measures of the thermal quantum correlation (TQC). And that the MID cannot completely replace the QD has been discovered. It is also observed that the DM interaction is a more optimal parameter than the inhomogeneous external magnetic field in the process of improving the TQC measured by QD and MID at the higher temperature. In addition, we note that the DM interaction and an inhomogeneous external magnetic field present remarkable different effects on the behavior of the QPT point at finite temperature.

Influence of Dzyaloshinskii–Moriya interaction on measurement-induced disturbance in a mixed-spin Heisenberg XXZ model with an inhomogeneous magnetic field

In this paper, by comparing with the thermal entanglement measured by negativity (N), we investigate the measurement-induced disturbance (MID) in a mixed-spin (1/2, 3/2) Heisenberg XXZ model with Dzyaloshinskii–Moriya (DM) interaction and an inhomogeneous external magnetic field. We make a comparison between MID and N, and find that their behaviors present obvious differences following the changes of the exchange constant J, DM interaction D, the uniform magnetic field B and the inhomogeneity of magnetic field b. It is found that J and D broaden the region of MID. At the same time, we notice that, for the case of small D, MID can detect the quantum phase transition near J=0, but not for N. It is also observed that DM interaction and the inhomogeneous external magnetic field play competing roles in enhancing the N and MID in our system. Moreover, we also note D is a more efficient parameter than B and b when adjusting MID under the higher temperature. In addition, we discover that, for the same parameters, the region of MID in our system is larger than the result in mixed-spin (1/2, 1) system.

Entanglement in Mixed-Spin (1/2, 3/2) Heisenberg XXZ Model with Dzyaloshinskii-Moriya Interaction

In this paper, the entanglement in a mixed-spin (1/2, 3/2) Heisenberg XXZ model with Dzyaloshinskii-Moriya (DM) interaction in an inhomogeneous external magnetic field is studied. We not only calculate the ground-state entanglement but also investigate the behaviors of quantum phase transition following the changes of DM interaction and nonuniform magnetic field. More importantly, we note that the DM interaction improves the critical magnetic field B c , the critical temperature T c and broadens the region of entanglement.

Entanglement and quantum teleportation in a three-qubit Heisenberg chain with three-site interactions

The thermal entanglement of a three-qubit XXZ Heisenberg model with three-site interactions in an external magnetic field, and the quantum teleportation via this model in thermal equilibrium state are investigated. It is found that entanglement and average fidelity depend on temperature, magnetic field, and anisotropy parameter $$J_Z$$JZ. Only ferromagnetic system is suitable for quantum teleportation. $$\hbox {XZX}+\hbox {YZY}$$XZX+YZY interaction is in favor of entanglement, average fidelity, and critical temperatures, while $$\text{ XZY }- \hbox {YZX}$$XZY-YZX interaction against all of them. Moreover, we also find entanglement does not fully reflect average fidelity in virtue of study the relation between entanglement and average fidelity.

Topological basis realization for BMW algebra and Heisenberg XXZ spin chain model

In this paper, we study three-dimensional (3D) reduced Birman–Murakami–Wenzl (BMW) algebra based on topological basis theory. Several examples of BMW algebra representations are reviewed. We also discuss a special solution of BMW algebra, which can be used to construct Heisenberg XXZ model. The theory of topological basis provides a useful method to solve quantum spin chain models. It is also shown that the ground state of XXZ spin chain is superposition state of topological basis.

Chern-Simons theory of magnetization plateaus of the spin-12quantum XXZ Heisenberg model on the kagome lattice

Frustrated spin systems on Kagome lattices have long been considered to be a promising candidate for realizing exotic spin liquid phases. Recently, there has been a lot of renewed interest in these systems with the discovery of materials such as Volborthite and Herbertsmithite that have Kagome like structures. In the presence of an external magnetic field, these frustrated systems can give rise to magnetization plateaus of which the plateau at $m=\frac{1}{3}$ is considered to be the most prominent. Here we study the problem of the antiferromagnetic spin-1/2 quantum XXZ Heisenberg model on a Kagome lattice by using a Jordan-Wigner transformation that maps the spins onto a problem of fermions coupled to a Chern-Simons gauge field. This mapping relies on being able to define a consistent Chern-Simons term on the lattice. Using a recently developed method to rigorously extend the Chern-Simons term to the frustrated Kagome lattice we can now formalize the Jordan-Wigner transformation on the Kagome lattice. We then discuss the possible phases that can arise at the mean-field level from this mapping and focus specifically on the case of $\frac{1}{3}$-filling ($m=\frac{1}{3}$ plateau) and analyze the effects of fluctuations in our theory. We show that in the regime of $XY$ anisotropy the ground state at the $1/3$ plateau is equivalent to a bosonic fractional quantum Hall Laughlin state with filling fraction $1/2$ and that at the $5/9$ plateau it is equivalent to the first bosonic Jain daughter state at filling fraction $2/3$.

Thermal entanglement in the mixed three-spin XXZ Heisenberg model on a triangular cell

We numerically investigate the thermal entanglements of spins (1/2, 1) and spins (1/2, 1/2) in the three-mixed (1/2, 1, 1/2) anisotropic Heisenberg XXZ spin system on a simple triangular cell under an inhomogeneous magnetic field. We show that the external magnetic field induces strong plateau formation in the pairwise thermal entanglement for fixed parameters of the Hamiltonian in the cases of ferromagnetic and antiferromagnetic interactions. We also observe an unexpected critical point at finite temperature in the thermal entanglement of spins (1/2, 1) for the antiferromagnetic case, while the entanglement of spins (1/2, 1) in the ferromagnetic case and the entanglement of spins (1/2, 1/2) in both ferromagnetic and antiferromagnetic cases almost decay exponentially to zero with increasing temperature. The critical point in the entanglement of spins (1/2, 1) in the antiferromagnetic case may be a signature of the quantum phase transition at finite temperature.

Impurity modes in the one-dimensional XXZ Heisenberg model

A Green's function formalism is used to calculate the energy of impurity modes associated with one and/or two magnetic impurities in the one-dimensional Heisenberg XXZ magnetic chain. The system can be tuned from the Heisenberg to the Ising model varying a parameter λ. A numerical study is performed showing two types of localized modes (s and p). The modes depend on λ and the degeneracy of the acoustic modes is broken.