Ising-Heisenberg Model Research Articles

Reducing the number of qubits in quantum simulations of one dimensional many-body Hamiltonians

We investigate the Ising and Heisenberg models using the block renormalization group method (BRGM), focusing on its behavior across different system sizes. The BRGM reduces the number of spins by a factor of 1/2 (1/3) for the Ising (Heisenberg) model, effectively preserving essential physical features of the model while using only a fraction of the spins. Through a comparative analysis, we demonstrate that as the system size increases, there is an exponential convergence between results obtained from the original and renormalized Ising Hamiltonians, provided the coupling constants are redefined accordingly. Remarkably, for a spin chain with 24 spins, all physical features, including magnetization, correlation function, and entanglement entropy, exhibit an exact correspondence with the results from the original Hamiltonian. The study of the Heisenberg model also shows this tendency, although complete convergence may appear for a size much larger than 24 spins, and is therefore beyond our computational capabilities. The success of BRGM in accurately characterizing the Ising model, even with a relatively small number of spins, underscores its robustness and utility in studying complex physical systems, and facilitates its simulation on current NISQ computers, where the available number of qubits is largely constrained.

From RVB to supersolidity: the saga of the Ising-Heisenberg model on the triangular lattice

From RVB to supersolidity: the saga of the Ising-Heisenberg model on the triangular lattice

Quantum magnetism in Fe2Cu2 polymeric branched chains: insights from exactly solved Ising-Heisenberg model

The spin-1/2 Ising-Heisenberg branched chain, inspired by the magnetic structure of three isostructural polymeric coordination compounds [(Tp)2Fe2(CN)6X (bdmap)Cu2(H2O)] ⋅ H2O to be further denoted as Fe2Cu2 (Tp = tris(pyrazolyl)hydroborate, bdmapH = 1,3-bis(dimethylamino)-2-propanol, HX = acetic acid, propionic acid or trifluoroacetic acid), is rigorously studied using the transfer-matrix method. The overall ground-state phase diagram reveals three distinct phases: a quantum antiferromagnetic phase, a quantum ferrimagnetic phase and a classical ferromagnetic phase. In the zero-temperature magnetization curve, two quantum ground states are manifested as intermediate plateaus at zero and half of the saturation magnetization, while the magnetization reaches its saturated value within the classical ferromagnetic phase. The bipartite entanglement between nearest-neighbor Heisenberg spins is more pronounced in the quantum ferrimagnetic phase compared to the quantum antiferromagnetic phase due to a fully polarized nature of the Ising spins. A reasonable agreement between theoretical predictions for the spin-1/2 Ising-Heisenberg branched chain and experimental data measured for a temperature dependence of the magnetic susceptibility and a low-temperature magnetization curve suggests strong antiferromagnetic coupling between nearest-neighbor Cu2+-Cu2+ magnetic ions and moderately strong ferromagnetic coupling between nearest-neighbor Cu2+-Fe3+ magnetic ions in the polymeric compounds Fe2Cu2. A thermal entanglement between nearest-neighbor Cu2+-Cu2+ magnetic ions persists up to a relatively high threshold temperature T ≈ 224 K and undergoes a transient magnetic-field-driven strengthening.

Generating Function for Projected Entangled-Pair States

Diagrammatic summation is a common bottleneck in modern applications of projected entangled-pair states, especially in computing low-energy excitations of a two-dimensional quantum many-body system. To solve this problem, here we extend the generating-function approach for tensor-network diagrammatic summation, a scheme previously proposed in the context of matrix product states. Taking the form of a one-particle excitation, we show that the excited state can be computed efficiently in the generating-function formalism, which can further be used in evaluating the dynamical structure factor of the system. Our benchmark results for the spin-1/2 transverse-field Ising model and Heisenberg model on the square lattice provide a desirable accuracy, showing good agreement with known results. We then study the spin-1/2J1-J2 model on the same lattice and investigate the dynamical properties of the putative gapless spin liquid phase. We conclude with a discussion on generalizations to multiparticle excitations. Published by the American Physical Society 2024

A possible coexistence of spontaneous magnetic order and thermal entanglement in a spin-1/2 Ising–Heisenberg diamond-decorated square lattice

The spin-1/2 Ising–Heisenberg model on a diamond-decorated square lattice is exactly solved by the decoration-iteration transformation, which establishes an exact mapping correspondence with the spin-1/2 Ising model on a square lattice with an effective temperature-dependent interaction between the nearest-neighbor spins. Exact results for the pair correlation function and spontaneous magnetization of the Heisenberg spins gained from the exact mapping equivalence allow a straightforward implementation of the concurrence, which may serve as a measure of the bipartite entanglement within decorating Heisenberg spin pairs. It is evidenced that the concurrence gradually diminishes upon increase of temperature above a disordered monomer-dimer ground state until it completely vanishes at a threshold temperature, while the concurrence is either always zero above a spontaneously ordered ferrimagnetic ground state or it shows a peculiar thermally assisted reentrance accompanied with a mutual coexistence of the spontaneous ferrimagnetic long-range order and the thermal entanglement.

Magnetization properties, super-stable points, and cycles of antiferromagnetic spin-1 diamond chains with nodal-nodal interactions

This study is devoted to the discovery of super-stable points and cycles in antiferromagnetic Ising and Ising-Heisenberg models with spin 1 on diamond chains with nodal-nodal interactions. These phenomena are important for understanding the complex behavior of magnetic systems. We specifically investigate their connection with magnetization plateaus, which serve as critical indicators of the model’s characteristics. Employing the recurrence relations technique, we derive multidimensional rational mappings that give insights about the statistical properties of the models. Carefully examining the stability properties of these mappings, in particular, by analyzing the maximum Lyapunov exponent, we have revealed the complex relationship between the magnetization plateau and dynamic properties. Throughout our extensive research, we have comprehensively studied the existence and behavior of super-stable points and cycles for various parameter configurations in spin-1 models on the diamond chains. By highlighting the basic properties of dynamics and stability, our research advances a fundamental understanding of complex magnetic systems and their fascinating properties.

Thermal first-order phase transitions, Ising critical points, and reentrance in the Ising-Heisenberg model on the diamond-decorated square lattice in a magnetic field

The thermal phase transitions of a spin-1/2 Ising-Heisenberg model on the diamond-decorated square lattice in a magnetic field are investigated using a decoration-iteration transformation and classical Monte Carlo simulations. A generalized decoration-iteration transformation maps this model exactly onto an effective classical Ising model on the square lattice with temperature-dependent effective nearest-neighbor interactions and magnetic field strength. The effective field vanishes along a ground-state phase boundary of the original model, separating a ferrimagnetic and a quantum monomer-dimer phase. At finite temperatures this phase boundary gives rise to an exactly solvable surface of discontinuous (first-order) phase transitions, which terminates in a line of Ising critical points. The existence of discontinuous reentrant phase transitions within a narrow parameter regime is reported and explained in terms of the low-energy excitations from both phases. These exact results, obtained from the mapping to the zero-field effective Ising model are corroborated by classical Monte Carlo simulations of the effective model.

The exact solution of the edge-modified graphene nanoribbon-like structure Ising-Heisenberg spin (1,1/2) system

A two-fold rotational symmetry ferromagnetic Ising-Heisenberg model modified by edge spin ( S = 1 / 2 ) with antiferromagnetic Heisenberg exchange interaction, whose shape is graphene nanoribbon-like has been constructed, and the host Ising spin ( S = 1 ). By use of the star-triangle transformation and the transfer matrix method, the edge states, thermodynamics and magnetization behavior of the system display various properties. The results perform that the unique edge-spin states and the host-spin states of the system are influenced with each other. And there are eleven different ground state phases, which are presented as the values of magnetic susceptibility multiplied by temperature at ultra-low temperature in the parameter space of single-ion anisotropy and antiferromagnetic Heisenberg interaction. Because of a large number of excited states close to the ground state, the specific heat curve shows multi-peak phenomena, which are analyzed by corresponding to the entropy of the system. The magnetization process of the system is complex, due to the direct correlation of the edge-spin states and the host-spin states of system, in which many different magnetization plateaus appear. The rigorous results of the number and width of magnetization plateaus and the saturation of the magnetization are written. This study offers unique opportunities for future technological applications such as proposed designs of graphene-based quantum spintronic devices as well as magnetic ordering.

Emergence of quantum spin frustration in spin-1/2 Ising-Heisenberg model on a decorated honeycomb lattice.

We study the spin-1/2 Ising-XXZ model on a decorated honeycomb lattice composed of five spins per unit cell, one Ising spin, and four Heisenberg spins. This model involving the Heisenberg exchange interaction is one of the few models that can be exactly solvable through the generalized star-triangle transformation. The significance of this model is its close relationship to the fully decorated quantum Heisenberg honeycomb lattice since 4/5 of the particles are Heisenberg spins. We investigate the phase diagram at zero temperature and identify a relevant quantum spin frustrated phase resulting from the contribution of quantum Heisenberg exchange interaction. We obtain an exact residual entropy for the quantum spin frustrated phase, which coincides with the residual entropy of the antiferromagnetic spin-1/2 Ising model on a triangular lattice. We also thoroughly explore its thermodynamic properties, focusing mainly on the frustrated region such as entropy, specific heat, spontaneous magnetization, and critical temperature under several conditions.

Unconventional spin frustration due to two competing ferromagnetic interactions of a spin-1/2 Ising-Heisenberg model on martini and martini-diced lattices.

The spin-1/2 Ising-Heisenberg model on martini and martini-diced lattices is exactly solved using a star-triangle transformation, which affords an exact mapping correspondence to an effective spin-1/2 Ising model on a triangular lattice. The ground-state phase diagram of both investigated quantum spin models display two spontaneously ordered ferromagnetic phases and one macroscopically degenerate disordered phase. In contrast to a classical ferromagnetic phase where the spontaneous magnetization of the Ising as well as Heisenberg spins acquire fully saturated values, the spontaneous magnetization of the Heisenberg spins is subject to a quantum reduction to one-third of its saturated value within a quantum ferromagnetic phase. The spontaneous magnetization and logarithmic divergence of the specific heat as the most essential features of both ferromagnetic phases disappear whenever the investigated quantum spin model is driven to the highly degenerate disordered phase. The disordered phase with nonzero residual entropy originates either from a geometric spin frustration caused by antiferromagnetic interactions or more strikingly it may also alternatively arise from a competition of the ferromagnetic Ising and Heisenberg interactions of easy-axis and easy-plane type, respectively. All three available ground states coexist together at a single triple point, around which anomalous magnetic and thermodynamic behavior can be detected.

Fractional magnetization plateaux of a spin-1/2 Heisenberg model on the Shastry-Sutherland lattice: effect of quantum XY interdimer coupling

Spin-1/2 Heisenberg model on the Shastry-Sutherland lattice is considered within the many-body perturbation theory developed from the exactly solved spin-1/2 Ising-Heisenberg model with the Heisenberg intradimer and Ising interdimer interactions. The former model is widely used for a description of magnetic properties of the layered compound SrCu_22(BO_33)_22, which exhibits a series of fractional magnetization plateaux at sufficiently low temperatures. Using the novel type of many-body perturbation theory we have found the effective model of interacting triplet excitations with the extended hard-core repulsion, which accurately recovers 1/8, 1/6 and 1/4 magnetization plateaux for moderate values of the interdimer coupling. A possible existence of a striking quantum phase of bound triplons is also revealed at low enough magnetic fields.

Ground State, Magnetization Process and Bipartite Quantum Entanglement of a Spin-1/2 Ising-Heisenberg Model on Planar Lattices of Interconnected Trigonal Bipyramids.

The ground state, magnetization scenario and the local bipartite quantum entanglement of a mixed spin- Ising–Heisenberg model in a magnetic field on planar lattices formed by identical corner-sharing bipyramidal plaquettes is examined by combining the exact analytical concept of generalized decoration-iteration mapping transformations with Monte Carlo simulations utilizing the Metropolis algorithm. The ground-state phase diagram of the model involves six different phases, namely, the standard ferrimagnetic phase, fully saturated phase, two unique quantum ferrimagnetic phases, and two macroscopically degenerate quantum ferrimagnetic phases with two chiral degrees of freedom of the Heisenberg triangular clusters. The diversity of ground-state spin arrangement is manifested themselves in seven different magnetization scenarios with one, two or three fractional plateaus whose values are determined by the number of corner-sharing plaquettes. The low-temperature values of the concurrence demonstrate that the bipartite quantum entanglement of the Heisenberg spins in quantum ferrimagnetic phases is field independent, but twice as strong if the Heisenberg spin arrangement is unique as it is two-fold degenerate.

Magnetic properties and phase diagrams of the mixed spin-(1 2, 3 2) Ising–Heisenberg model in the mean field approximation

In this paper, the effects of the longitudinal [Formula: see text] and the transverse [Formula: see text] crystal fields on the mixed spin-[Formula: see text] Ising–Heisenberg model have been studied. The thermodynamic properties of the model are obtained by using a new approach of the mean field approximation (MFA). The thermal variations of the order-parameters and the total magnetic susceptibility of the model are carefully investigated to obtain the phase diagrams on the [Formula: see text] planes for [Formula: see text] and on the [Formula: see text] planes for [Formula: see text] and 6. The existence of compensation temperatures between the sublattice magnetizations, [Formula: see text], and the two components of the quadrupole moments, [Formula: see text], are observed. Our results are compared with other existing works in the literature and reliable agreements are found.

Purifying Deep Boltzmann Machines for Thermal Quantum States

We develop two cutting-edge approaches to construct deep neural networks representing the purified finite-temperature states of quantum many-body systems. Both methods commonly aim to represent the Gibbs state by a highly expressive neural-network wave function, exemplifying the idea of purification. The first method is an entirely deterministic approach to generate deep Boltzmann machines representing the purified Gibbs state exactly. This strongly assures the remarkable flexibility of the ansatz which can fully exploit the quantum-to-classical mapping. The second method employs stochastic sampling to optimize the network parameters such that the imaginary time evolution is well approximated within the expressibility of neural networks. Numerical demonstrations for transverse-field Ising models and Heisenberg models show that our methods are powerful enough to investigate the finite-temperature properties of strongly correlated quantum many-body systems, even when the problematic effect of frustration is present.

Enhanced magnetocaloric effect in a mixed spin-(1/2, 1) Ising–Heisenberg two-leg ladder with strong–rung interaction

The magnetic and magnetocaloric properties of the mixed spin-(1/2,1) Ising-Heisenberg model on a two-leg ladder with dimer-rung alternation are exactly examined under an adiabatic demagnetization process using the transfer-matrix formalism. We notify that the magnetization curve of the model exhibits plateaux as a function of the applied magnetic field and cyclic four-spin Ising interaction at certain rational fractions of the saturation value. We precisely investigate the ability of cooling/heating of the model nearby the critical points at which discontinuous ground-state phase transition occurs. It is evidenced that the model manifests an enhanced magnetocaloric effect in a proximity of the magnetization steps and jumps, accompanying with the plateaux and jumps of correlation function of the dimer spins. We conclude that not only the cooling/heating capability of the model could be pleasantly demonstrated by the applied magnetic field variations, but also a typical cyclic four-spin Ising interaction plays essential role to determine an efficiency of the magnetocaloric effect of the model.

A Conjecture on the Relationship Between Critical Residual Entropy and Finite Temperature Pseudo-transitions of One-dimensional Models

Recently pseudo-critical temperature clues were observed in one-dimensional spin models, such as the Ising-Heisenberg spin models, among others. Here we report a relationship between the zero-temperature phase boundary residual entropy (critical residual entropy) and pseudo-transition. Usually, the residual entropy increases in the phase boundary, which means the system becomes more degenerate at the phase boundary compared with its adjacent states. However, this is not always the case; at zero temperature, there are some phase boundaries where the entropy holds the largest residual entropy of the adjacent states. Therefore, we can propose the following conjecture: If residual entropy at zero temperature is a continuous function at least from the one-sided limit at a critical point, then pseudo-transition evidence will appear at finite temperature near the critical point. We expect that this argument would apply to study more realistic models. Only by analyzing the residual entropy at zero temperature, one could identify a priori whether the system will exhibit the pseudo-transition at finite temperature. To strengthen our conjecture, we use two examples of Ising-Heisenberg models, which exhibit pseudo-transition behavior: one frustrated coupled tetrahedral chain and another unfrustrated diamond chain.

Nature of intermediate magnetization plateaus of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice resembling a triangulated kagome lattice.

The spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice is exactly solved in a magnetic field within the framework of the generalized star-triangle transformation and the method of exact recursion relations. The generalized star-triangle transformation establishes an exact mapping correspondence with the effective spin-1/2 Ising model on a triangular Husimi lattice with a temperature-dependent field, pair and triplet interactions, which is subsequently rigorously treated by making use of exact recursion relations. The ground-state phase diagram of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice, which bears a close resemblance with a triangulated kagomé lattice, involves, in total, two classical and three quantum ground states manifested in respective low-temperature magnetization curves as intermediate plateaus at 1/9, 1/3, and 5/9 of the saturation magnetization. It is verified that the fractional magnetization plateaus of quantum nature have character of either dimerized or trimerized ground states. A low-temperature magnetization curve of the spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice resembling a triangulated kagome lattice may exhibit either no intermediate plateau, a single 1/3 plateau, a single 5/9 plateau, or a sequence of 1/9, 1/3, and 5/9 plateaus depending on a character and relative size of two considered coupling constants.

Unsaturated Bipartite Entanglement of a Spin-1/2 Ising-Heisenberg Model on a Triangulated Husimi Lattice

A bipartite entanglement between two nearest-neighbor Heisenberg spins of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice is quantified using a concurrence. It is shown that the concurrence equals zero in a classical ferromagnetic and a quantum disordered phase, while it becomes sizable though unsaturated in a quantum ferromagnetic phase. A thermally-assisted reentrance of the concurrence is found above a classical ferromagnetic phase, whereas a quantum ferromagnetic phase displays a striking cusp of the concurrence at a critical temperature.

New cluster approximation for Ising systems

A new cluster approximation based on the effective field theory for Ising systems is presented. The application of the presented method to the most basic model, namely the spin-1/2 Ising model has been carried out. Obtained critical temperatures for spin-1/2 Ising model improves the results of Bethe-Pierls approximation. Generalization of this approximation to the other spin models such as higher spin Ising model and Heisenberg model, that are capable of explaining the magnetic properties of the real materials have been discussed.

Large magnetocaloric effect and critical behavior in Cu-doped nanocrystalline La0.7Te0.3Mn1-yCuyO3 (0.1 ≤ y ≤ 0.5)

The impact of copper doping on the magnetic properties and critical behavior of the nanocrystalline La0.7Te0.3Mn1-yCuyO3 (0.1 ≤ y ≤ 0.5) system has been explored. The powder X-ray diffraction (XRD) patterns affirmed the single crystal phase for all samples without any detectable secondary phase. We have observed rhombohedral (R3‾c space group) crystal symmetry for y ≤ 0.3. With the increase in copper doping composition (y = 0.4 and 0.5) structure changes to orthorhombic (Pbnm space group). The temperature-dependent magnetization data suggests a paramagnetic (PM) to ferromagnetic (FM) phase transition upon cooling for all compositions. The Curie temperature TC is almost constant (about 226 K) for the compositions y ≤ 0.3 and after that TC decreases from 154 K (y = 0.4) to 91 K (y = 0.5). The maximal values of magnetic entropy change |ΔSMmax| were obtained from a series of magnetic isotherms and were observed to be 4.59 J/(kg-K), 4.84 J/(kg-K), 3.92 J/(kg-K), 2.49 J/(kg-K) and 1.56 J/(kg-K) for y = 0.1, 0.2, 0.3, 0.4 and 0.5 respectively up to a field change of 5 T. The critical behavior at PM-FM transition for all the samples was studied and reliability of the obtained critical exponents was checked using scaling hypothesis. The critical exponents deduced in this study were observed to follow the mean field, 3D Ising and 3D Heisenberg model.