Dimensional Spin Systems Research Articles

Soliton solutions in (2 + 1)-dimensional integrable spin systems: an investigation of the Myrzakulov–Lakshmanan equation-II

Soliton solutions in (2 + 1)-dimensional integrable spin systems: an investigation of the Myrzakulov–Lakshmanan equation-II

Magnetic relaxation in a Co(II) based quasi-one dimensional Ising spin system

Single crystal study of Co(NCS)2(aniline)2 reveals that this compound orders at 6.49 K into a canted AF magnetic structure that explains the presence of a hysteresis loop along the b crystal direction. Effective s=1/2 spins of Co(II) ions within the ground state doublet create an Ising spin system that can be described by J1−J2 triangular model. Temperature dependence of specific heat yields exchange interactions J1=31.3(4) K and 2J2=−2.23(7) K. Applying magnetic field ≃6 kOe perpendicular to b compensates for the AF exchange J2 decoupling ferromagnetic spin chains. This restores the one-dimensionality of the system and allows for observation of magnetic relaxation of single chains, similar to previously studied pyridine-based Co(NCS)2L2 compounds. The analysis of the relaxation time is performed taking into account single-ion relaxation mechanisms together with the Glauber relaxation. We also show, using Monte Carlo calculations of specific heat, that for ferromagnetic J1≫|J2|, the triangular Ising model can be approximated by the rectangular Ising model for which the analytical Onsager’s solution is available.

Quasi discreteness analysis of a two dimensional ferromagnetic spin system

By introducing bilinear and anisotropic interactions in a model based on a square lattice of ferromagnetism, we learn about the influence of excitations with nonlinearity in intrinsic localized modes (ILMS) and modulational instability. Equations of motion are constructed in the semi-classical limit by pairing Glauber’s coherent state representation with the Dyson-Maleev form of spin operators. A Cubic Nonlinear Schrödinger (CNLS) equation is obtained using an intensive method of quasi-discreteness analysis mixed with a method of multiple scales. We also analyze the bright envelope solitons and intrinsically localized modes using a Sine-Cosine function approach. Stability conditions are obtained using Modulational Instability analysis.

Universality Class of Ising Critical States with Long-Range Losses.

We show that spatial resolved dissipation can act on d-dimensional spin systems in the Ising universality class by qualitatively modifying the nature of their critical points. We consider power-law decaying spin losses with a Lindbladian spectrum closing at small momenta as ∝q^{α}, with α a positive tunable exponent directly related to the power-law decay of the spatial profile of losses at long distances, 1/r^{(α+d)}. This yields a class of soft modes asymptotically decoupled from dissipation at small momenta, which are responsible for the emergence of a critical scaling regime ascribable to the nonunitary counterpart of the universality class of long-range interacting Ising models. For α<1 we find a nonequilibrium critical point ruled by a dynamical field theory described by a Langevin model with coexisting inertial (∼∂_{t}^{2}) and frictional (∼∂_{t}) kinetic coefficients, and driven by a gapless Markovian noise with variance ∝q^{α} at small momenta. This effective field theory is beyond the Halperin-Hohenberg description of dynamical criticality, and its critical exponents differ from their unitary long-range counterparts. Our Letter lays out perspectives for a revision of universality in driven open systems by employing dark states tailored by programmable dissipation.

Geometric approach to Lieb-Schultz-Mattis theorem without translation symmetry under inversion or rotation symmetry

We propose a geometric {approach to Lieb-Schultz-Mattis theorem for} quantum many-body systems with discrete spin-rotation symmetries and lattice inversion or rotation symmetry, but without translation symmetry assumed. Under symmetry-twisting on a $(d-1)$-dimensional plane, we find that any $d$-dimensional inversion-symmetric spin system possesses a doubly degenerate spectrum when it hosts a half-integer spin at the inversion-symmetric point. We also show that any rotation-symmetric generalized spin model with a projective representation at the rotation center has a similar degeneracy under symmetry-twisting. We argue that these degeneracies imply that {a unique symmetric gapped ground state that is smoothly connected to product states} is forbidden in the original untwisted systems -- generalized inversional/rotational Lieb-Schultz-Mattis theorems without lattice translation symmetry imposed. The traditional Lieb-Schultz-Mattis theorems with translations also fit in the proposed framework.

Holographic quantum algorithms for simulating correlated spin systems

We present a suite of ``holographic'' quantum algorithms for efficient ground-state preparation and dynamical evolution of correlated spin systems, which require far fewer qubits than the number of spins being simulated. The algorithms exploit the equivalence between matrix-product states (MPS) and quantum channels, along with partial measurement and qubit reuse, in order to simulate a $D$-dimensional spin system using only a $(D\ensuremath{-}1)$-dimensional subset of qubits along with an ancillary qubit register whose size scales logarithmically in the amount of entanglement present in the simulated state. Ground states can either be directly prepared from a known MPS representation or obtained via a holographic variational quantum eigensolver (holoVQE). Dynamics of MPS under local Hamiltonians for time $t$ can also be simulated with an additional (multiplicative) $\mathrm{poly}(t)$ overhead in qubit resources. These techniques open the door to efficient quantum simulation of MPS with exponentially large bond dimension, including ground states of two- and three-dimensional systems, or thermalizing dynamics with rapid entanglement growth. As a demonstration of the potential resource savings, we implement a holoVQE simulation of the antiferromagnetic Heisenberg chain on a trapped-ion quantum computer, achieving within $10(3)%$ of the exact ground-state energy of an infinite chain using only a pair of qubits.

Dirac-like Hamiltonians associated to Schrödinger factorizations

In this work, we have extended the factorization method of scalar shape-invariant Schrödinger Hamiltonians to a class of Dirac-like matrix Hamiltonians. The intertwining operators of the Schrödinger equations have been implemented in the Dirac-like shape invariant equations. We have considered also another kind of anti-intertwining operators changing the sign of energy. The Dirac-like Hamiltonians can be obtained from reduction of higher dimensional spin systems. Two examples have been worked out, one obtained from the sphere \({{\mathcal {S}}}^2\) and a second one, having a non-Hermitian character, from the hyperbolic space \({{\mathcal {H}}}^2\).

Undecidability of the Spectral Gap in One Dimension

The spectral gap problem - determining whether the energy spectrum of a system has an energy gap above ground state, or if there is a continuous range of low-energy excitations - pervades quantum many-body physics. Recently, this important problem was shown to be undecidable for quantum spin systems in two (or more) spatial dimensions: there exists no algorithm that determines in general whether a system is gapped or gapless, a result which has many unexpected consequences for the physics of such systems. However, there are many indications that one dimensional spin systems are simpler than their higher-dimensional counterparts: for example, they cannot have thermal phase transitions or topological order, and there exist highly-effective numerical algorithms such as DMRG - and even provably polynomial-time ones - for gapped 1D systems, exploiting the fact that such systems obey an entropy area-law. Furthermore, the spectral gap undecidability construction crucially relied on aperiodic tilings, which are not possible in 1D. So does the spectral gap problem become decidable in 1D? In this paper we prove this is not the case, by constructing a family of 1D spin chains with translationally-invariant nearest neighbour interactions for which no algorithm can determine the presence of a spectral gap. This not only proves that the spectral gap of 1D systems is just as intractable as in higher dimensions, but also predicts the existence of qualitatively new types of complex physics in 1D spin chains. In particular, it implies there are 1D systems with constant spectral gap and non-degenerate classical ground state for all systems sizes up to an uncomputably large size, whereupon they switch to a gapless behaviour with dense spectrum.

Gapless spin liquid in a square-kagome lattice antiferromagnet

Observation of a quantum spin liquid (QSL) state is one of the most important goals in condensed-matter physics, as well as the development of new spintronic devices that support next-generation industries. The QSL in two dimensional quantum spin systems is expected to be due to geometrical magnetic frustration, and thus a kagome-based lattice is the most probable playground for QSL. Here, we report the first experimental results of the QSL state on a square-kagome quantum antiferromagnet, KCu6AlBiO4(SO4)5Cl. Comprehensive experimental studies via magnetic susceptibility, magnetisation, heat capacity, muon spin relaxation (μSR), and inelastic neutron scattering (INS) measurements reveal the formation of a gapless QSL at very low temperatures close to the ground state. The QSL behavior cannot be explained fully by a frustrated Heisenberg model with nearest-neighbor exchange interactions, providing a theoretical challenge to unveil the nature of the QSL state.

Effective negative specific heat by destabilization of metastable states in dipolar systems.

We study dipolarly coupled three-dimensional spin systems in both the microcanonical and the canonical ensembles by introducing appropriate numerical methods to determine the microcanonical temperature and by realizing a canonical model of heat bath. In the microcanonical ensemble, we show the existence of a branch of stable antiferromagnetic states in the low-energy region. Other metastable ferromagnetic states exist in this region: by externally perturbing them, an effective negative specific heat is obtained. In the canonical ensemble, for low temperatures, the same metastable states are unstable and reach a new branch of more robust metastable states which is distinct from the stable one. Our statistical physics approach allows us to put some order in the complex structure of stable and metastable states of dipolar systems.

Origin of the slow growth of entanglement entropy in long-range interacting spin systems

Long-range interactions allow far-distance quantum correlations to build up very fast. Nevertheless, numerical simulations demonstrated a dramatic slowdown of entanglement entropy growth after a sudden quench. In this work, we unveil the general mechanism underlying this counterintuitive phenomenon for $d$-dimensional quantum spin systems with slowly-decaying interactions. We demonstrate that the semiclassical rate of collective spin squeezing governs the dynamics of entanglement, leading to a universal logarithmic growth in the absence of semiclassical chaos. In fact, the standard quasiparticle contribution is shown to get suppressed as the interaction range is sufficiently increased. All our analytical results agree with numerical computations for quantum Ising chains with long-range couplings. Our findings thus identify a qualitative change in the entanglement production induced by long-range interactions, and are experimentally relevant for accessing entanglement in highly-controllable platforms, including trapped ions, atomic condensates and cavity-QED systems.

Experimental investigation of low dimensional spin system in metal oxides

Nano particles of SrCrO4 were manufactured by sol-gel technique. The crystal part ofSrCrO4 is monoclinic having space group P21/n. We calcined it at 950°C temperature. Its cand a lattice parameter are 6.77 and 7.08 which is very close to the reported ones. Ba and Cadoped SrCrO4 were also synthesized by sol-gel method by various concentrations for x= 0.2,0.4, 0.6 and 0.8. Doping samples also sintered at 950°C for 2 hours in order to obtain finepowder. Different characterization techniques such as XRD, Ultra-violet-Spectroscopy, PLSpectroscopy and FTIR Spectroscopy were used to analyze SrCrO4, Ba and Ca-dopedSrCrO4. XRD tells us about the crystal size and dislocation density of samples. The value of2? for the XRD patterns is ranging from 5 to 95. Four peaks are observed in the UV-spectraof SrCrO4 which occur at 350nm, 380nm, 700nm and 750nm. The UV band gap of SrCrO4is 3.25 eV. In PL spectra, two peaks are observed one at 480nm and other at 410nm. At480nm, the energy of emitted photons is 2.5eV, while at 410nm the emitted photons hasenergy of 3ev. In the FTIR analysis, the core modes frequently showed by CrO4 unit aresymmetric stretching bond (?1 (A1)), symmetric bending mode (?2 (E)), asymmetricstretching mode (?3 (F2)) and asymmetric bending mode (?4 (F2)).

Magnetocaloric effect as a signature of quantum level-crossing for a spin-gapped system

Recent research dealing with magnetocaloric effect (MCE) study of antiferromagnetic (AFM) low dimensional spin systems have revealed a number of fascinating ground-state crossover characteristics upon application of external magnetic field. Herein, through MCE investigation we have explored field-induced quantum level-crossing characteristics of one such spin system: (NCP), an AFM spin 1/2 dimer. Experimental magnetization and specific heat data are presented and the data have been employed to evaluate entropy, magnetic energy and magnetocaloric properties. We witness a sign change in magnetic Grüneisen parameter across the level-crossing field BC. An adiabatic cooling is observed at low temperature by tracing the isentropic curves in temperature-magnetic field plane. Energy-level crossover characteristics in NCP interpreted through MCE analysis are well consistent with the observations made from magnetization and specific heat data.

Ergodicity variation in a long range interacting one-dimensional Ising spin system subject to a time-varying magnetic field

We consider one dimensional Ising spin system in a transverse uniform time-dependent magnetic field. The asymptotic behavior of the bipartite entanglements between the terminal spin and each one of the other spins along the chain is investigated and compared at different spin-spin interaction ranges, from nearest neighbor to infinite long range, under the separate action of two different magnetic fields, constant and time-varying. We find that each of the nearest neighbor and next to nearest neighbor bipartite entanglements reach an asymptotic final state that is independent of the initial condition or the variation in the interaction range showing perfect ergodic behavior at quite short interaction ranges. However, the nearest neighbor entanglement maintains this behavior at a slightly longer ranges. The other bipartite entanglements assume a zero value within these interaction ranges. At intermediate short and long interaction ranges, the asymptotic states of all entanglements become strongly dependent on the initial state and the interaction range, deviating from the ergodic behavior observed before. The maximum asymptotic entanglement attainable between a pair of spins takes place at a long interaction range value that increases with the distance between the spins. At the infinite long range interaction, the dynamics of all bipartite entanglements coincide. great care should be taken in constructing both.

Lieb-Schultz-Mattis theorem and its generalizations from the perspective of the symmetry-protected topological phase

We ask whether a local Hamiltonian with a featureless (fully gapped and nondegenerate) ground state could exist in certain quantum spin systems. We address this question by mapping the vicinity of certain quantum critical point (or gapless phase) of the $d-$dimensional spin system under study to the boundary of a $(d+1)-$dimensional bulk state, and the lattice symmetry of the spin system acts as an on-site symmetry in the field theory that describes both the selected critical point of the spin system, and the corresponding boundary state of the $(d+1)-$dimensional bulk. If the symmetry action of the field theory is nonanomalous, i.e. the corresponding bulk state is a trivial state instead of a bosonic symmetry protected topological (SPT) state, then a featureless ground state of the spin system is allowed; if the corresponding bulk state is indeed a nontrivial SPT state, then it likely excludes the existence of a featureless ground state of the spin system. From this perspective we identify the spin systems with SU($N$) and SO($N$) symmetries on one, two and three dimensional lattices that permit a featureless ground state. We also verify our conclusions by other methods, including an explicit construction of these featureless spin states.

Thermal Entanglement in XXZ Heisenberg Model for Coupled Spin-Half and Spin-One Triangular Cell

In this paper, we investigate the thermal entanglement of two-spin subsystems in an ensemble of coupled spin-half and spin-one triangular cells, (1/2, 1/2, 1/2), (1/2, 1, 1/2), (1, 1/2, 1) and (1, 1, 1) with the XXZ anisotropic Heisenberg model subjected to an external homogeneous magnetic field. We adopt the generalized concurrence as the measure of entanglement which is a good indicator of the thermal entanglement and the critical points in the mixed higher dimensional spin systems. We observe that in the near vicinity of the absolute zero, the concurrence measure is symmetric with respect to zero magnetic field and changes abruptly from a non-null to null value for a critical magnetic field that can be signature of a quantum phase transition at finite temperature. The analysis of concurrence versus temperature shows that there exists a critical temperature, that depends on the type of the interaction, i.e. ferromagnetic or antiferromagnetic, the anisotropy parameter and the strength of the magnetic field. Results show that the pairwise thermal entanglement depends on the third spin which affects the maximum value of the concurrence at absolute zero and at quantum critical points.

Optical phonon dynamics and electronic fluctuations in the Dirac semimetal Cd3As2

Raman scattering in the three-dimensional Dirac semimetal $\mathrm{C}{\mathrm{d}}_{3}\mathrm{A}{\mathrm{s}}_{2}$ shows an intricate interplay of electronic and phonon degrees of freedom. We observe resonant phonon scattering due to interband transitions, an anomalous anharmonicity of phonon frequency and intensity, as well as quasielastic $(E\ensuremath{\sim}0)$ electronic scattering. The latter two effects are governed by a characteristic temperature scale ${T}^{*}\ensuremath{\sim}100\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ that is related to mutual fluctuations of lattice and electronic degrees of freedom. A refined analysis shows that this characteristic temperature corresponds to the energy of optical phonons which couple to interband transitions in the Dirac states of $\mathrm{C}{\mathrm{d}}_{3}\mathrm{A}{\mathrm{s}}_{2}$. As electron-phonon coupling in a topological semimetal is primarily related to phonons with finite momenta, the back action on the optical phonons is only observed as anharmonicities via multiphonon processes involving a broad range of momenta. The resulting energy density fluctuations of the coupled system have previously only been observed in low dimensional or frustrated spin systems with suppressed long range ordering.

Holographic encoding of universality in corner spectra

In numerical simulations of classical and quantum lattice systems, 2d corner transfer matrices (CTMs) and 3d corner tensors (CTs) are a useful tool to compute approximate contractions of infinite-size tensor networks. In this paper we show how the numerical CTMs and CTs can be used, {\it additionally\/}, to extract universal information from their spectra. We provide examples of this for classical and quantum systems, in 1d, 2d and 3d. Our results provide, in particular, practical evidence for a wide variety of models of the correspondence between $d$-dimensional quantum and $(d+1)$-dimensional classical spin systems. We show also how corner properties can be used to pinpoint quantum phase transitions, topological or not, without the need for observables. Moreover, for a chiral topological PEPS we show by examples that corner tensors can be used to extract the entanglement spectrum of half a system, with the expected symmetries of the $SU(2)_k$ Wess-Zumino-Witten model describing its gapless edge for $k=1,2$. We also review the theory behind the quantum-classical correspondence for spin systems, and provide a new numerical scheme for quantum state renormalization in 2d using CTs. Our results show that bulk information of a lattice system is encoded holographically in efficiently-computable properties of its corners.

Joint Density of States Calculation Employing Wang–Landau Algorithm

Joint density of states (JDoS), which depends both on energy and another variable like order parameter provides more information than the conventional density of states (DoS) which depend only on energy. Calculation of JDoS requires huge computational time. In this paper we employ two level method to calculate JDoS which requires relatively much less computational time. We demonstrate this method on a two dimensional Ising spin system, lattice spin model of double strand DNA (dsDNA) and Heisenberg ferromagnet.

General dichotomization procedure to provide qudit entanglement criteria

We present a general strategy to derive entanglement criteria which consists in performing a mapping from qudits to qubits that preserves the separability of the parties and SU(2) rotational invariance. Consequently, it is possible to apply the well known positive partial transpose criterion to reveal the existence of quantum correlations between qudits. We discuss some examples of entangled states that are detected using the proposed strategy. Finally, we demonstrate, using our scheme, how some variance-based entanglement witnesses can be generalized from qubits to higher dimensional spin systems.