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Spin 1/2 quantum spin chains represent the prototypical model for coupled two-level systems. Consequently, they offer a fertile playground for both fundamental and technological applications ranging from the theory of thermalization to quantum computation. Recently, it has been shown that interesting phenomena are associated to the boundary conditions imposed on the quantum spin chains via the so-called topological frustration. In this work, we analyze the effects of such frustration on a few-spin system, with a particular focus on the strong even–odd effects induced in the ground-state energy. We then implement a topologically frustrated quantum spin chain on a quantum computer to show that our predictions are visible on current quantum hardware platforms. [ABSTRACT FROM AUTHOR]

Spin network (SN) systems can be used to achieve quantum state transfer with high fidelity and to generate entanglement. A new approach to design spin‐chain‐based spin network systems, for short‐range quantum information processing and phase‐sensing, has been proposed recently in Advanced Quantum Technologies. In this paper, the scalability of such systems is investigated, by designing larger SN systems that can be used for longer‐range quantum information tasks, such as connecting together quantum processors. Furthermore, more complex SN designs, which can produce different types of entangled states, are presented. Simulations of disorder effects show that even such larger SN systems are robust against realistic levels of disorder. [ABSTRACT FROM AUTHOR]

Spin 1/2 quantum spin chains represent the prototypical model for coupled two-level systems. Consequently, they offer a fertile playground for both fundamental and technological applications ranging from the theory of thermalization to quantum computation. Recently, it has been shown that interesting phenomena are associated to the boundary conditions imposed on the quantum spin chains via the so-called topological frustration. In this work, we analyze the effects of such frustration on a few-spin system, with a particular focus on the strong even–odd effects induced in the ground-state energy. We then implement a topologically frustrated quantum spin chain on a quantum computer to show that our predictions are visible on current quantum hardware platforms.

The transmission of a qubit in a tight-binding channel with exponentially decaying hopping terms and diagonal disorder is investigated. The end sites act as sender and receiver and are perturbatively coupled to the channel. This is done to suppress interference of the channel modes during the time evolution of the state. We explore the performance of the transfer fidelity against the disorder strength and hopping range within the channel. The scaling behavior of the participation number as a function of the hopping range is also discussed. Channels featuring long-range interactions display distinct robustness against disorder and high-quality quantum state transfer is attainable even for disorder levels of the order of the largest hopping amplitude. [ABSTRACT FROM AUTHOR]

This paper addresses the approximation of fractional harmonic maps. Besides a unit-length constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness results for critical points of the fractional Dirichlet energy on unit-length vector fields. We devise and analyze numerical methods for the approximation of various partial differential equations related to fractional harmonic maps. The compactness results imply the convergence of numerical approximations. Numerical examples on spin chain dynamics and point defects are presented to demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

We address quantum characterization of anisotropic spin chains in the presence of anti-symmetric exchange, and investigate whether the Hamiltonian parameters of the chain may be estimated with precision approaching the ultimate limit imposed by quantum mechanics. At variance with previous approaches, we focus on the information that may be extracted by measuring only two neighboring spins rather than a global observable on the entire chain. We evaluate the Fisher information (FI) of a two-spin magnetization measure, and the corresponding quantum Fisher information (QFI), for all the relevant parameters, i.e. the spin coupling, the anisotropy, and the Dzyaloshinskii–Moriya (DM) parameter. Our results show that the reduced system made of two neighboring spins may be indeed exploited as a probe to characterize global properties of the entire system. In particular, we find that the ratio between the FI and the QFI is close to unit for a large range of the coupling values. The DM coupling is beneficial for coupling estimation, since it leads to the presence of additional bumps and peaks in the FI and QFI, which are not present in a model that neglects exchange interaction and may be exploited to increase the robustness of the overall estimation procedure. Finally, we address the multiparameter estimation problem, and show that the model is compatible but sloppy, i.e. both the Uhlmann curvature and the determinant of the QFI matrix vanish. Physically, this means that the state of the system actually depends only on a reduced numbers of combinations of parameters, and not on all of them separately.

We investigate quantum phase transitions (QPTs) in various spin chain systems using the multipartite entanglement measure $\tau_\mathrm{SEF}$ based on the monogamy inequality of squared entanglement of formation (EOF). Our results demonstrate that $\tau_\mathrm{SEF}$ is more effective and reliable than bipartite entanglement or bipartite correlation measures such as EOF, von Neumann entropy, and quantum discord in characterizing QPTs. $\tau_\mathrm{SEF}$ not only detects critical points that may go unnoticed by other detectors but also avoids the issue of singularity at non-critical points encountered by other measures. Furthermore, by applying $\tau_\mathrm{SEF}$ , we have obtained the phase diagram for the XY spin chain with three and four interactions and discovered a new quantum phase.

Quantum state transfer (QST) plays a central role in the field of quantum computation and communication, but its quality will be deteriorated by the ubiquitous variations and noise in quantum systems. Here we propose robust and nonadiabatic protocols for transmitting quantum state across a strongly coupled spin chain, especially in the presence of unwanted disorders in the couplings. To this end, we approximately map the low-energy subspaces of the odd-size Heisenberg chain to a two-level system, and derive the sensitivity of the final fidelity with respect to systematic deviations or time-varying fluctuations. Subsequently, leveraging the flexibility of the inverse-engineering technique, we optimize the state-transfer robustness concerning these perturbations individually. The resulting schemes allow for more stable QST than the original accelerated schemes and only require manipulating the two boundary couplings instead of the whole system, which open up the possibility of fast and robust information transfer in spin-based quantum systems.

We address spin transport in the easy-axis Heisenberg spin chain subject to different integrability-breaking perturbations. We find subdiffusive spin transport characterized by dynamical exponent z = 4 up to a timescale parametrically long in the anisotropy. In the limit of infinite anisotropy, transport is subdiffusive at all times; for finite anisotropy, one eventually recovers diffusion at late times but with a diffusion constant independent of the strength of the perturbation and solely fixed by the value of the anisotropy. We provide numerical evidence for these findings, and we show how they can be understood in terms of the dynamical screening of the relevant quasiparticle excitations and effective dynamical constraints. Our results show that the diffusion constant of near-integrable diffusive spin chains is generically not perturbative in the integrability-breaking strength. [ABSTRACT FROM AUTHOR]

We investigate the propagation of local bipartite quantum correlations, along with the tripartite mutual information to characterize the information scrambling through dynamical evolution of spin chains. Starting from an initial state with the first pair of spins in a Bell state, we study how quantum correlations spread to other parts of the system, using different representative spin Hamiltonians, viz. the Heisenberg Model, a spin-conserving model, the transverse-field XY model, a non-conserving but integrable model, and the kicked Harper model, a spin conserving but nonintegrable model. We show that the local correlations spread consistently in the case of spin-conserving dynamics in both integrable and nonintegrable cases, with a strictly nonnegative tripartite mutual information. In contrast, in the case of non-conserving dynamics, tripartite mutual information is negative and local pair correlations do not propagate. [ABSTRACT FROM AUTHOR]

Spin chains can be used to describe a wide range of platforms for quantum computation and quantum information. They enable the understanding, demonstration, and modeling of numerous useful phenomena, such as high fidelity transfer of quantum states, creation and distribution of entanglement, and creation of resources for measurement‐based quantum processing. In this paper, a more complex spin system, a 2D spin network (SN) engineered by applying suitable unitaries to two uncoupled spin chains, is studied. Considering only the single‐excitation subspace of the SN, it is demonstrated that the system can be operated as a router, directing information through the SN. It is also shown that it can serve to generate maximally entangled states between two sites. Furthermore, it is illustrated that this SN system can be used as a sensor device able to determine an unknown phase applied to a system spin. A detailed modeling investigation of the effects of static disorder in the system shows that this system is robust against different types of disorder. [ABSTRACT FROM AUTHOR]

One-dimensional (1D) magnets are of great interest owing to their intriguing quantum phenomena and potential application in quantum computing. We successfully synthesized an ideal antiferromagnetic spin S = 5/2 chain compound [H2(4,4'-bpy)](H3O)2Fe2F10 (4,4'-bpy = 4,4'-bipyridyl) 1, using a single-step low-temperature hydrothermal method under conditions that favors the protonation of the bulky bidentate ligand 4,4'-bpy. Compound 1 consists of well-separated (Fe3+-F-)¥ chains with a large Fe-F-Fe angle of 174.8°. Both magnetic susceptibility and specific heat measurements show that 1 does not undergo a magnetic long-range ordering down to 0.5 K, despite the strong Fe-F-Fe intrachain spin exchange J with J/kB = -16.2(1) K. This indicates a negligibly weak interchain spin exchange J'. The J'/J value estimated for 1 is extremely small (< 2.8×10-6), smaller than those reported for all other S = 5/2 chain magnets. Our hydrothermal synthesis incorporates both [H2(4,4'-bpy)]2+ and (H3O)+ cations into the crystal lattice with numerous hydrogen bonds, hence effectively separating the (Fe3+-F-)¥ spin chains. This single-step hydrothermal synthesis under conditions favoring the protonation of bulky bidentate ligands offers an effective synthetic strategy to prepare well-separated 1D spin chain systems of magnetic ions with various spin values., (© 2024 Wiley‐VCH GmbH.)

The conception of almost complete revivals has been introduced recently. In a quantum many-body system local observable may exhibit an almost complete revival to its maximal value at the predetermined moment of time. In this paper we extend the original procedure such that the revival may be from an arbitrary point on the Bloch sphere to the arbitrary point. Furthermore in the proposed procedure the reviving and collapsing sites are not necessarily the same. We also demonstrate that for spins higher than almost complete revivals are suppressed as . [ABSTRACT FROM AUTHOR]

We study the decoherence process induced by a spin chain environment on a central spin consisting of R spins and we apply it on the dynamics of quantum correlations (QCs) of three interacting qubits. To see the impact of the initially prepared state of the spin chain environment on the decoherence process, we assume the spin chain environment prepared in two main ways, namely, either the ground state or the vacuum state in the momentum space. We develop a general heuristic analysis when the spin chain environment is prepared in these states, to understand the decoherence process against the physical parameters. We show that the decoherence process is mainly determined by the choice of the initially prepared state, the number of spins of the chain, the coupling strength, the anisotropy parameter and the position from the quantum critical point. In fact, in the strong coupling regime, the decoherence process does not appear for the environment prepared in the vacuum state and it behaves oscillatory in the case of evolution from the ground state. On the other hand, in the weak coupling regime and far from the quantum critical point, decoherence induced by the ground state is weaker than that of the vacuum state. Finally, we show that QCs are completely shielded from decoherence in the case of evolution from the W state and obey the same dynamics as the decoherence factors for the GHZ state. [ABSTRACT FROM AUTHOR]

Many real-world tasks include some kind of parameter estimation, i.e. the determination of a parameter encoded in a probability distribution. Often, such probability distributions arise from stochastic processes. For a stationary stochastic process with temporal correlations, the random variables that constitute it are identically distributed but not independent. This is the case, for instance, for quantum continuous measurements. In this article, we derive the asymptotic Fisher information rate for a stationary process with finite Markov order. We give a precise expression for this rate which is determined by the process’ conditional distribution up to its Markov order. Second, we demonstrate with suitable examples that correlations may both enhance or hamper the metrological precision. Indeed, unlike for entropic information quantities, in general nothing can be said about the sub- or super-additivity of the joint Fisher information in the presence of correlations. To illustrate our results, we apply them to thermometry on an Ising spin chain, considering nearest-neighbour and next-to-nearest neighbour coupling. In this case, the asymptotic Fisher information rate is directly connected to the specific heat capacity of the spin chain. We observe that the presence of correlations strongly enhances the estimation precision in an anti-ferromagnetic chain, while in a ferromagnetic chain this is not the case.

As noisy intermediate‐scale quantum (NISQ) devices grow in number of qubits, determining good or even adequate parameter configurations for a given application, or for device calibration, becomes a cumbersome task. An evolutionary algorithm is presented here which allows for the automatic tuning of the parameters of any arrangement of coupled qubits, to perform a given task with high fidelity. The algorithm's use is exemplified with the generation of schemes for the distribution of quantum states and the design of multi‐qubit gates. The algorithm is demonstrated to converge very rapidly, yielding unforeseeable designs of quantum devices that perform their required tasks with excellent fidelities. Given these promising results, practical scalability, and application versatility, the approach has the potential to become a powerful technique to aid the design and calibration of NISQ devices. [ABSTRACT FROM AUTHOR]

A finite chain of thirty‐one paramagnetic centers is reported, synthesized by reaction of hydrated chromium fluoride, copper carbonate and pivalic acid in the presence of 1,4,7,10‐tetrazacyclododecane (cyclen). Magnetic studies show predominantly anti‐ferromagnetic exchange leading to a high density of low‐lying spin states and large saturation field. [ABSTRACT FROM AUTHOR]

The new compound Ba9V3S11(S2)2.was synthesized using high pressure and high temperature. The single crystal XRD based structure solution and refinement show that it crystallizes in the hexagonal system with the space group P-6c2 (188) and the lattice parameters a=9.1979(4) Å and c=18.0462(10) Å. Its onedimensional structure is related to the high-pressure phase Ba9V3Se15 (Ba9V3Se11(Se2)2) and consists of chains made of face-sharing VS6 octahedra running along the c-axis. The chains contain two distinct sites of Vanadium with a mixed valence state of V3+ and V2+. The space between the chains, two type of columns, is occupied by disulfides (S2) 2- pairs and isolated sulfide anions S2- surrounded by Ba2+ cations. The distributions within the columns are slightly different than in Ba9V3Se11(Se2)2 making the two compounds not strictly isostructural but analogues with the same symmetry and unit cell. We discuss this phase on the basis of crystallochemical analysis and DFT calculated electronic structure. Assuming a magnetic insulator as found from DFT+U calculations, we discuss the existence of magnetic clusters within the spin chains. [ABSTRACT FROM AUTHOR]

The new compound Ba9V3S11(S2)2.was synthesized using high pressure and high temperature. The single crystal XRD based structure solution and refinement show that it crystallizes in the hexagonal system with the space group P-6c2 (188) and the lattice parameters a=9.1979(4) Å and c=18.0462(10) Å. Its onedimensional structure is related to the high-pressure phase Ba9V3Se15 (Ba9V3Se11(Se2)2) and consists of chains made of face-sharing VS6 octahedra running along the c-axis. The chains contain two distinct sites of Vanadium with a mixed valence state of V3+ and V2+. The space between the chains, two type of columns, is occupied by disulfides (S2) 2- pairs and isolated sulfide anions S2- surrounded by Ba2+ cations. The distributions within the columns are slightly different than in Ba9V3Se11(Se2)2 making the two compounds not strictly isostructural but analogues with the same symmetry and unit cell. We discuss this phase on the basis of crystallochemical analysis and DFT calculated electronic structure. Assuming a magnetic insulator as found from DFT+U calculations, we discuss the existence of magnetic clusters within the spin chains. [ABSTRACT FROM AUTHOR]

Based on quantum renormalization group (QRG) method, we investigated quantum coherence and quantum phase transition (QPT) in XXZ chain and XY chain, respectively. The results show that both the geometric quantum coherence and entropic coherecne can accurately indicate the QPT at critical point after enough iteration steps. Moreover, the increasing anisotropy parameter destroys the coherence in the XXZ chain, while enhances it in the XY chain. In addition, focused on the XXZ chain we analyzed the nonanalytic phenomena and scaling behaviors with different theoretical exponents in detail. [ABSTRACT FROM AUTHOR]

In the present paper, we study the quantum phase transition in a spin-1 Heisenberg model with two and three particles by using pairwise classical and quantum thermal correlations and entanglement measures, that is, the generalized concurrence and the negativity at finite temperatures. We have used thermodynamic functions of particle number and particle susceptibility to characterize the thermodynamical behavior. The pairwise correlations are derived based on a necessary and sufficient condition for the zero-discord state. We obtain analytical results for the coherence-vector representation of a bipartite state. Using the exact diagonalization technique, we demonstrate that the quantum critical points, detected by the particle number and the particle susceptibility, are ultimately in close correspondence to that of thermal pairwise correlations and entanglement measures. [ABSTRACT FROM AUTHOR]

This paper describes two cases of interaction between a quantized electromagnetic field and two different XY spin molecules; one with spins 12, and the other with spins 1. Both interact with a quantized electromagnetic field, with one of the spins in the chain interacting with the electromagnetic field. The interaction between the field mode and the spin chain with spins 1 is described by the one- and two-photon Jaynes-Cummings model (JC model). On the other hand, the interaction between the spins 12 and the electromagnetic field is described only by the one-photon Jaynes-Cummings model. Analytical and numerical calculations were made for the case of a different number of photons in the field mode, a different number of spins, and a different position of spin, interacting with the electromagnetic field. The invariant and block structures of such a chain are shown with a comparison made between the evolution of the magnetic moment and the number of photons in both cases. [ABSTRACT FROM AUTHOR]

The J1 - J3 Heisenberg spin models with nearest-neighbor (J1) and additional isotropic three-site (J3) spin interactions remain relatively less explored, although such types of competing exchange terms can naturally emerge from different sources, including the strong-coupling expansion of the multiorbital Hubbard model. Below we present a short survey of the recently published research in this field, the emphasis being on the characteristics of the varietyofquantum phases supported bya fewgenericuniform-and alternating-spin J1 - J3 Heisenbergchains. Forthe reason that the positive (J3 > 0)three-site couplings tend towards the formation of local quantum dimers, the J1 - J3 spin models typically experience some spontaneous dimerization upon increasing J3. Actually, it occurred that the established dimer phases in spin-S J1 - J3 Heisenberg chains (S > 1/2) serve as complete analogues of the famous gapped Majumdar-Ghosh dimer phase in the spin-1/2 Heisenberg chain with next-nearest-neighbor couplings. The same dimerizations have been observed in the alternating-spin (S, a) Ji - J3 chains (S > a), provided that the cell spin S + a = integer, whereas for halfinteger cell spin, the local dimer formation produces gapless spin-liquid ground states. The alternating-spin J1 - J3 chains also provide some typical examples of spin models supporting the so-called non-Lieb-Mattis magnetic phases. [ABSTRACT FROM AUTHOR]

There has been some substantial research about the connections between quantum chaos and quantum correlations in many‐body systems. This paper discusses a specific aspect of correlations in chaotic spin models, through concurrence (CC) and quantum discord (QD). Numerical results obtained in the quantum chaos regime and in the integrable regime of spin‐1/2 chains are compared. The CC and QD between nearest‐neighbor pairs of spins are calculated for all energy eigenstates. The results show that, depending on whether the system is in a chaotic or integrable regime, the distribution of CC and QD are markedly different. On the other hand, in the integrable regime, states with the largest CC and QD are found in the middle of the spectrum, in the chaotic regime, the states with the strongest correlations are found at low and high energies at the edges of spectrum. Finite‐size effects are analyzed, and some of the results are discussed in the light of the eigenstate thermalization hypothesis. [ABSTRACT FROM AUTHOR]

We investigate quantum-phase transitions (QPT) in the Ising transverse field model, the XY-Heisenberg model with staggered Dzyaloshinskii–Moriya (DM) interaction, and the bond alternating Ising model with DM interaction, on a one-dimensional periodic chain using the quantum renormalization group (QRG) method. Based on l 1 -norm and relative entropy, we employ two quantum coherence measures to identify QPT. Our results show that the QPT can be characterized by the coherence measure calculated for each QRG step. It is found that after large number of QRG iterations, the coherence in the ground state develops two saturated values corresponding to two different phases and changes abruptly at a quantum critical point (QCP). The scaling behavior of the system is investigated by computing the derivative of the coherence measure around the QCP that shows a logarithmic dependence on the length of the chain. The critical exponent of the correlation length is also calculated. [ABSTRACT FROM AUTHOR]

We study here the short-time behavior of the spectral form factor for chain-like many-body systems of arbitrary length N, an important tool to distinguish chaotic and integrable dynamics. We found in the past that while the long-time behavior of the spectral form factor is universal and follows predictions by Random Matrix Theory, it becomes highly system dependent for short times, even for large N in the disorder-free case. Now, our aim is to study to which extend this observation persists if a nonzero disorder is considered. [ABSTRACT FROM AUTHOR]

Such problems as computation of spectra of spin chains and vibrational spectra of molecules can be written as high-dimensional eigenvalue problems , i.e., when the eigenvector can be naturally represented as a multidimensional tensor. Tensor methods have proven to be an efficient tool for the approximation of solutions of high-dimensional eigenvalue problems, however, their performance deteriorates quickly when the number of eigenstates to be computed increases. We address this issue by designing a new algorithm motivated by the ideas of Riemannian optimization (optimization on smooth manifolds) for the approximation of multiple eigenstates in the tensor-train format , which is also known as matrix product state representation. The proposed algorithm is implemented in TensorFlow, which allows for both CPU and GPU parallelization. [ABSTRACT FROM AUTHOR]

We consider transformation from a closed to an open spin chain and vice versa produced by changing single link strength in a pair of neighboring spins. We show that in the non-adiabatic time domain fidelity of such a process can be increased by proper choosing of the control function for spin-spin exchange coupling. We obtain this function for an antiferromagnetic quantum Ising chain and present heuristic reasons restricting possible timedependences of Hamiltonians applied for a high-fidelity control. [ABSTRACT FROM AUTHOR]

We use the fermion-current basis in the space of local operators for the computation of the expectation values for the integrable spin chain of spins 1. Our main tool consists in expressing a given local operator in the fermion-current basis. For this, we use the same method as in the spin-1/2 case which is based on the arbitrariness of the Matsubara data. [ABSTRACT FROM AUTHOR]

Abstract A comparative study of pairwise quantum coherence, quantum and classical correlations is addressed for non-nearest spin pairs of the 1D Heisenberg spin- 1 2 XX chain. Following the Jordan–Wigner mapping, we diagonalize the hamiltonian of the chain and we check this procedure numerically as well. Using the "Pauli basis expansion" formalism we get the pairwise quantities studied in this work at any distance. We then, show the role of quantum correlations in revealing quantum phase transitions, the robustness of quantum discord to the temperature and the dominance of quantum correlations over their classical counterpart in the magnetic and thermal interval in quantum spin chains. We conclude the paper by shedding light from a resource-driven point of view on the new born quantity "quantum coherence" where we discuss its role in detecting quantum phase transitions being a long-range quantity, and how it outclasses the usual quantum correlations measures in the robustness against the temperature, which indicates potential uses in the framework of quantum information processing. Highlights • Behavior of quantum coherence, quantum and classical correlations between spin pairs at different lattice spacing in the XX model is studied. • Interplay between quantum coherence and quantum correlations is discussed. • Quantum coherence and quantum correlations can detect quantum phase transitions in the XX model. • Potential role of quantum coherence in performing quantum information processing task. [ABSTRACT FROM AUTHOR]

We report on heat capacity measurements performed on a large Sr2Ca12Cu24O41 single crystal in the temperature range between 0.07 and 20 K and magnetic fields up to 10 T. A transition into the antiferromagnetic ground state is observed at TN=2.8 K. The heat capacity becomes strongly time-dependent below 0.5 K due to a Schottky contribution typical for materials with charge or spin-density waves. We found a quasi-linear contribution to the heat capacity that can be attributed to weakly coupled and shifted antiferromagnetic spin chains along the a-direction. [ABSTRACT FROM AUTHOR]

A protocol for fast and robust magnon transport in a one-dimensional spin chain is devised. Employing an approximate mapping between the chain and a single harmonically trapped particle, we exploit the known analytic control protocols for the latter and adopt them to achieve fast, high-fidelity transport in the chain. We compare the performance with finite time adiabatic protocols, showing that the designed scheme allows for significantly faster and more stable transport. Furthermore, we show that a sharp transition exists between regions in which the protocol is effective and when it breaks down, giving rise to a heuristic speed limit for the process.

The J_1-J_3 Heisenberg spin models with nearest-neighbor (J_1) and additional isotropic three-site (J_3) spin interactions remain relatively less explored, although such types of competing exchange terms can naturally emerge from different sources, including the strong-coupling expansion of the multiorbital Hubbard model. Below we present a short survey of the recently published research in this field, the emphasis being on the characteristics of the variety of quantum phases supported by a few generic uniform- and alternating-spin J_1-J_3 Heisenberg chains. For the reason that the positive (J_3>0) three-site couplings tend towards the formation of local quantum dimers, the J_1-J_3 spin models typically experience some spontaneous dimerization upon increasing J_3. Actually, it occurred that the established dimer phases in spin-S J_1-J_3 Heisenberg chains (S>1/2) serve as complete analogues of the famous gapped Majumdar-Ghosh dimer phase in the spin-1/2 Heisenberg chain with next-nearest-neighbor couplings. The same dimerizations have been observed in the alternating-spin (S, σ) J_1-J_3 chains (S>σ), provided that the cell spin S+σ= integer, whereas for half-integer cell spin, the local dimer formation produces gapless spin-liquid ground states. The alternating-spin J_1-J_3 chains also provide some typical examples of spin models supporting the so-called non-Lieb-Mattis magnetic phases.

This paper describes two cases of interaction between a quantized electromagnetic field and two different XY spin molecules; one with spins ½, and the other with spins 1. Both interact with a quantized electromagnetic field, with one of the spins in the chain interacting with the electromagnetic field. The interaction between the field mode and the spin chain with spins 1 is described by the one- and two-photon Jaynes-Cummings model (JC model). On the other hand, the interaction between the spins ½ and the electromagnetic field is described only by the one-photon Jaynes-Cummings model. Analytical and numerical calculations were made for the case of a different number of photons in the field mode, a different number of spins, and a different position of spin, interacting with the electromagnetic field. The invariant and block structures of such a chain are shown with a comparison made between the evolution of the magnetic moment and the number of photons in both cases.

In XXZ chains with large enough interactions, spin transport can be significantly suppressed when the bias of the dissipative driving becomes large enough. This phenomenon of negative differential conductance is caused by the formation of two oppositely polarized ferromagnetic domains at the edges of the chain. Here, we show that this many-body effect, combined with a non-uniform magnetic field, can allow for a high degree of control of the spin current. In particular, by studying all of the possible shapes of local magnetic fields potentials, we find that a configuration in which the magnetic field points up for half of the chain and down for the other half, can result in giant spin-current rectification, for example, up to 108 for a system with only 8 spins. Our results show clear indications that the rectification can increase with the system size.