Low-dimensional Quantum Spin Systems Research Articles

Exact solution of two-dimensional (2D) Ising model with a transverse field: A low-dimensional quantum spin system

The exact solution of ferromagnetic two-dimensional (2D) Ising model with a transverse field, which can be used to describe the critical phenomena in low-dimensional quantum spin systems, is derived by equivalence between the ferromagnetic 2D Ising model with a transverse field and the ferromagnetic three-dimensional (3D) Ising model. The results obtained in this work can be extended to be suitable for the antiferromagnetic 2D Ising model with a transverse field in the cases without frustration.

Classes of topological qubits from low-dimensional quantum spin systems

Topological phases of matter is a natural place for encoding robust qubits for quantum computation. In this work we extend the newly introduced class of qubits based on valence-bond solid models with SPT (symmetry-protected topological) order to more general cases. Furthermore, we define and compare various classes of topological qubits encoded in the bulk ground states of topological systems, including SSB (spontaneous symmetry-breaking), TOP (topological), SET (symmetry-enriched topological), SPT, and subsystem SPT classes. We focus on several features for qubits to be robust, including error sets, logical support, code distance and shape of logical gates. In particular, when a global U(1) symmetry is present and preserved, we find a twist operator that extracts the SPT order plays the role of a topological logical operator, which is suitable for global implementation.

Ground-state and magnetization behavior of the frustrated spin-1/2 antisymmetric diamond chain

The low-dimensional quantum spin systems have been extensively studied in the past three decades due to the novel ground states and rich magnetic behaviors,especially the quantum spin chain with diamond topology structure. Motivated by recent experimental success in Cu3(CO3)2(OH)2 compound,which is regarded as a model material of spin-1/2 diamond chain,researchers have paid a lot of attention to various variants of diamond spin chains.In this paper,we mainly examine the magnetic properties of an antisymmetric spin-1/2 Ising-Heisenberg diamond chain with the secondneighbor interaction between nodal spins.By using exact diagonalization and transfer-matrix methods,the ground-state phase diagram,magnetization behavior and macroscopic thermodynamics are exactly solved for the particular case that all magnetic bonds yield antiferromagnetic couplings,which usually shows the most interesting magnetic features closely related to a striking interplay between geometric frustration and quantum fluctuations.To clearly illustrate the effect of second-neighbor interaction item,we consider a highly frustrated situation that all Ising-Heisenberg bonds and Heisenberg bonds possess the same interaction strength.The calculation results indicate that the second-neighbor interaction item will enrich ground states and magnetization plateaus.A classical ferrimagnetic phase FRI1 corresponding to a novel two-thirds of intermediate plateau with translationally broken symmetry is introduced,manifesting itself as up-up-up-down-up-up spin configuration at a ground-state.In addition,there are other four distinct ground states which can be identified from the phase diagram,i.e.,one saturated paramagnetic phase SP,one classical ferrimagnetic phase FRI2,one quantum ferrimagnetic phase QFI and the unique quantum antiferromagnetic phase QAF.The classical phase FRI2 and quantum phase QFI both generate one-third of magnetization plateau.It is worth mentioning that all the values of these magnetization plateaus satisfy the Oshikawa-Yamanaka-Affleck condition.Besides,the results also have shown a rich variety of temperature dependence of total magnetization and specific heat.The magnetization displays the remarkable thermal-induced changes as the external field is sufficiently close to critical value where two or more than two different ground states coexist.At the critical field relevant to a coexistence of two different states,the total magnetization displays a monotonic decrease trend.The thermal dependence of zero-field specific heat displays relative complex variations for different second-neighbor interactions between nodal spins.At first,the specific heat presents only a single rounded Schottky-type maximum.Using the second-neighbor interaction,another sharp peak arises at low-temperature and is superimposed on this round maximum,and the specific heat exhibits a double-peak structure. On further strengthening,the low-temperature one keeps its height shifting towards high temperature,while the hightemperature round peak suffers great enhancement and moves in an opposite direction.Finally,the low temperature peak entirely merges with the Schottky-type peak at a certain value of second-neighbor interaction,and above this value, the specific curve recovers its single peak structure.The observed double-peak specific heat curves mainly originate from thermal excitations between the ground-state spin configuration QAF and the ones close enough in energy to the ground state.

Crystal Growth of Cu6(Ge,Si)6O18·6H2O and Assignment of UV-VIS Spectra in Comparison to Dehydrated Dioptase and Selected Cu(II) Oxo-Compounds Including Cuprates

Low-dimensional quantum spin systems with the Cu2+ central ion are still in the focus of experimental and theoretical research. Here is reported on growth of mm-sized single-crystals of the low-dimensional S = 1/2 spin compound Cu6(Ge,Si)6O18·6H2O by a diffusion technique in aqueous solution. A route to form Si-rich crystals down to possible dioptase, the pure silicate, is discussed. Motivated by previously reported incorrect assignments of UV-VIS spectra, the assignment of dd excitations from such spectra of the hexahydrate and the fully dehydrated compound is proposed in comparison to dioptase and selected Cu(II) oxo-compounds using bond strength considerations. Non-doped cuprates as layer compounds show higher excitation energies than the title compound. However, when the antiferromagnetic interaction energy as Jz·ln(2) is taken into account for cuprates, a single linear relationship between the Dqe excitation energy and equatorial Cu(II)-O bond strength is confirmed for all compounds. A linear representation is also confirmed between 2A1g energies and a function of axial and equatorial Cu-O bond distances if auxiliary axial bonds are used for four-coordinated compounds. The quotient Dt/Ds of experimental orbital energies deviating from the general trend to smaller values indicates the existence of H2O respectively Cl− axial ligands in comparison to oxo-ligands, whereas larger Dt/Dqe values indicate missing axial bonds. The quotient of the excitation energy 2A1g by 2·2Eg-2B2g allows checking for correctness of the assignment and to distinguish between axial oxo-ligands and others like H2O or Cl−.

Large-scale single-crystal growth of (CH3)2NH2CuCl3 for neutron scattering experiments

Neutron scattering studies on low-dimensional quantum spin systems require large-size single-crystals. Single-crystals of (CH3)2NH2CuCl3 showing low-dimensional magnetic behaviors were grown by a slow solvent evaporation method in a two-solvent system at different temperature settings. The best results were obtained for the bilayer solution of methanol and isopropanol with a molar ratio of 2:1 at 35°C. The quality of the obtained single-crystals was tested by powder and single-crystal X-ray diffraction and single-crystal neutron diffraction. In addition, to confirm structural phase transitions (SPTs), thermal analysis and single-crystal X-ray diffraction at 300K and 175K, respectively, were conducted, confirming the presence of a SPT at Tup=288K on heating and Tdown=285K on cooling.

Electronic structure of spin systems

Low-dimensional quantum spin systems, characterized by their unconventional magnetic properties, have attracted much attention. Synthesis of materials appropriate to various classes within these systems has made this field very attractive and a site of many activities. The experimental results like susceptibility data are fitted with the theoretical model to derive the underlying spin Hamiltonian. However, often such a fitting procedure which requires correct guess of the assumed spin Hamiltonian leads to ambiguity in deciding the representative model. In this review article, we will describe how electronic structure calculation within the framework of Nth order muffin-tin orbital (NMTO) based Wannier function technique can be utilized to identify the underlying spin model for a large number of such compounds. We will show examples from compounds belonging to vanadates and cuprates.

Possible Phase Transition and Band Gap Closing in Photoexcited Semiconductor CeZn3P3

In f -electron systems, external fields, such as a magnetic field, and pressure play crucial roles in changing the electronic state, for example, in magnetic-field-induced valence transition and pressure-induced superconductivity. Optical light is another attractive external field source. For d-electron systems, many interesting phenomena, i.e., photoinduced metallic states in Mott insulators, photoinduced magnetization, and a photoinduced change in spin configuration, have been reported. The effects of light illumination on f -electron systems have been extensively studied for Eu chalcogenides. A photoinduced metal– insulator transition and a photoinduced magnetization have already been reported. However, the effects of light illumination on other f -electron systems have not been thoroughly studied. In this paper, the investigation of photoinduced phenomena in a Ce-based semiconductor, CeZn3P3, 12) is reported. CeZn3P3 crystallizes into a hexagonal ScAl3C3-type structure, in which Ce atoms form a two-dimensional triangular lattice. CeZn3P3 and other ScAl3C3-type compounds, such as YbAl3C3, are attracting much attention as low-dimensional quantum spin systems. A sintered polycrystalline sample was prepared by a standard solid-state-reaction technique. The product was evaluated using the powder X-ray diffraction pattern and found to show an almost single phase with a small amount of unknown impurities. The fundamental band gap of CeZn3P3 was estimated using the diffuse reflectance Rd spectrum (0.5–4 eV), which was obtained using a UV–visible spectrometer (Shimadzu UV-3600). After calculating the Kubelka–Munk function f ðRdÞ corresponding to the absorption coefficient, 1⁄2h f ðRdÞ 1=n (h : photon energy) was obtained, as shown in the inset of Fig. 1. Following the report on the indirectgap semiconductor SmZn3P3, 18) we employed n 1⁄4 2. The band gap of 0.365 eV was determined by the tangential line (see the solid line in the inset of Fig. 1) at the initial increase in 1⁄2h f ðRdÞ . The temperature dependence of electrical resistivity ðT Þ between 30 and 300K under light illumination was measured by a conventional DC four-probe method using a closed-cycle He gas cryostat. The optical source was a laser diode with a photon energy of 1.85 eV, which is sufficient for exciting electrons across the band gap. A parallelepiped sample with dimensions of 1:25 1:6 10 mm was cut from a pellet of CeZn3P3. The distance between the voltage electrodes was 3.5mm. All electrodes were covered by metal plates to reduce extrinsic photovoltaic effects. The optical light from the laser diode was focused on the area between the voltage electrodes. Figure 1 shows the measurement history of ðT Þ. Three alternating measurements of ðT Þ with light turned off and on were carried out. All ðT Þ curves show no thermal hysteresis. We kept the light on for data acquisition (about 7 h for one cycle between 300 and 30K). The illumination with a fluence rate of 4.5W/cm transformed the ðT Þ of the virgin sample denoted as 1st (0W/cm) into a nonsemiconducting ðT Þ with a sharp anomaly at Ta 1⁄4 240K. When we turned off the light, although the semiconducting behavior was recovered, the ðT Þ value was not perfectly reproduced [see ðT Þ denoted as 2nd (0W/cm)]. The nonsemiconducting behavior with a sharp anomaly appeared again when we illuminated the sample; however, the optical power necessary to reproduce the anomaly increased and Ta decreased. The third measurement without light also showed a decrease in ðT Þ compared with that of the second one. In the third measurement with light [3rd (15W/cm)], we could not observe the sharp anomaly, even under the maximum fluence rate. Although intense light gradually damaged the sample, ðT Þ under light illumination exhibited a marked increase in carrier number. The ðT Þ with the sharp anomaly at Ta suggests that a photoinduced phase transition is expected to occur. Further studies are required to clarify the origin of the anomaly. The increase in the temperature of the sample caused by the optical illumination is expected to be small, at least above 50K, since ðT Þ for 2nd (15W/cm) is nearly identical to that for 1st (4.5W/cm) with a different fluence rate. Between the measurements of ðT Þ for 2nd (0W/cm) and ðT Þ for 2nd (15W/cm), the fluence rate dependence of ðT Þ was measured (see Fig. 2). Below 11W/cm, the recovery of ðT Þ without light was carefully examined. ðT Þ with 3W/cm showed a weak anomaly at approximately 240K, which may be a precursor of a phase transition. The temperature of the anomaly decreased to 210K with increasing fluence rate (see the arrows in Fig. 2). When the fluence rate was increased, the gradual inhibition of the semiconducting behavior, resulting in decreased ðT Þ Fig. 1. (Color online) Measurement history of ðT Þ of CeZn3P3. The inset shows the plot of 1⁄2h f ðRdÞ 1=2 vs h . Journal of the Physical Society of Japan 82 (2013) 125001

Experimental quantification of entanglement through heat capacity

A new experimental realization of heat capacity as an entanglement witness is reported. Entanglement properties of a low–dimensional quantum spin system are investigated by heat capacity measurements performed down to very low temperatures (400 mK), for various applied magnetic field values. The experimentally extracted results for the value of heat capacity at zero field matches perfectly with the theoretical estimates of entanglement from model Hamiltonians. The studied sample is a spin half antiferromagnetic system that shows a clear signature of quantum phase transition at very low temperatures when the heat capacity is varied as a function of fields at a fixed temperature. The variation of entanglement as a function of field is then explored in the vicinity of the quantum phase transition to capture the sudden loss of entanglement.

Nonergodic classical correlations lead to ergodic quantum correlations in low-dimensional spin models

Quantum correlations are traditionally viewed as constituted out of classical correlations and single-party parameters. While this, of course, remains so, we show that entanglement can have statistical mechanical properties like ergodicity, which are not inherited from the corresponding classical correlations and single-party parameters, in diagonalizable as well as nondiagonalizable low-dimensional quantum spin systems. In particular, we find that the results hold for the quantum XY spin models on the chain, ladder and in two dimensions.

Experimental detection of quantum information sharing and its quantification in quantum spin systems

We study the macroscopic entanglement properties of a low-dimensional quantum spin system by investigating its magnetic properties at low temperatures and high magnetic fields. The spin system chosen for this is copper nitrate (Cu(NO3)2 × 2.5H2O), which is a spin chain that exhibits dimerization. The temperature and magnetic field dependence of entanglement from the susceptibility and magnetization data are given, by comparing the experimental results with the theoretical estimates. Extraction of entanglement has been made possible through the macroscopic witness operator, magnetic susceptibility. An explicit comparison of the experimental extraction of entanglement with theoretical estimates is provided. It was found that theory and experiments match over a wide range of temperatures and fields. The spin system studied exhibits quantum phase transition (QPT) at low temperatures when the magnetic field is swept through a critical value. We show explicitly for the first time, using tools used in quantum information processing, that QPT can be captured experimentally using quantum complementary observables, which clearly delineate entangled states from separable ones across the QPT. We have also estimated the partial information sharing in this system from our magnetization and susceptibility data. The complementarity relation has been experimentally verified to hold in this system.

Deconfined quantum criticality and logarithmic violations of scaling from emergent gauge symmetry

We demonstrate that the low-energy effective theory for a deconfined quantum critical point in $d=2+1$ dimensions contains a leading-order contribution given by the Faddeev-Skyrme model. The Faddeev-Skyrme term is shown to give rise to the crucial Maxwell term in the CP${}^{1}$ field theory governing the deconfined quantum critical point. We derive the leading contribution to the spin stiffness near the quantum critical point and show that it exhibits a logarithmic correction to scaling of the same type as recently observed numerically in low-dimensional models of quantum spin systems featuring a quantum critical point separating an antiferromagnetically ordered state from a valence bond solid state. These corrections, appearing away from upper or lower critical dimensions, reflect an emergent gauge symmetry of low-dimensional antiferromagnetic quantum spin systems.

Ab initiostudy of low-dimensional quantum spin systemsSr3NiPtO6,Sr3CuPtO6, andSr3NiIrO6

Using first-principles density-functional theory, we investigate the electronic structure of a class of low-dimensional quantum spin systems of general formula ${A}_{3}B{B}^{\ensuremath{'}}{\text{O}}_{6}$, which has drawn recent interest due to their intriguing magnetic properties. In our study, we focus on three compounds, ${\text{Sr}}_{3}{\text{NiPtO}}_{6}$, ${\text{Sr}}_{3}{\text{CuPtO}}_{6}$, and ${\text{Sr}}_{3}{\text{NiIrO}}_{6}$, formed from choices of $3d$ and $5d$ elements in $B$ and ${B}^{\ensuremath{'}}$ sites. Based on our first-principles calculations, we derive the magnetic interactions and the single-ion anisotropies, which define the underlying spin models for the three compounds. Our study forms the basis for future investigations.

Spin-Peierls transition in low-dimensional quantum spin systems: a Green’s function approach

We study the spin-Peierls (SP) transition of one-dimensional chain polymeric complexes coupled to lattice by means of many-body Green's function theory. The chain effective elastic constant is an intrinsic factor that determines the order of SP transition. It is found that the SP transition temperature T(SP) and the susceptibility-maximum temperature T(max) are in agreement with the experimental results. When an external magnetic field is applied to the chain, it makes T(SP) and T(max) decrease, and drives the SP transition from the second order to the first order. Besides, we show that the two-site thermal entanglement entropy is a good indicator of SP transition. Further considering the effect of interchain coupling on SP transition, with weak coupling of double-chain, the theoretical values are closer to the experimental results. We also calculate the density of states and spectral functions, which show that the energy gap vanishes at a critical temperature lower than T(SP), indicating a gapless SP phase lies in the gapped dimerized phase. The interchain coupling can drive the SP transition from the second order to the first order, while the SP dimerization may collapse for large interchain couplings.

Vector Chiral States in Low-Dimensional Quantum-Spin Systems

A class of exact spin ground states with nonzero averages of vector spin chirality, $<\v{S}_i \times \v{S}_j \cdot \hat{z}>$, is presented. It is obtained by applying non-uniform O(2) rotations of spin operators in the XY plane on the SU(2)-invariant Affleck-Kennedy-Lieb-Tasaki (AKLT) states and their parent Hamiltonians. Excitation energies of the new ground states are studied with the use of single-mode approximation in one dimension for S=1. The excitation gap remains robust. Construction of chiral AKLT states is shown to be possible in higher dimensions. We also present a general idea to produce vector chirality-condensed ground states as non-uniform O(2) rotations of the non-chiral parent states. Dzyaloshinskii-Moriya interaction is shown to imply non-zero spin chirality.

Thermal conductivity due to spins in low-dimensional quantum spin systems

Thermal conductivity due to spins in low-dimensional quantum spin systems

Dynamical spin chirality and spin anisotropy inSr14Cu24O41: A neutron polarization analysis study

Low-dimensional quantum spin systems constitute an ideal built-in laboratory to study fundamental aspects of solid-state physics. By engineering suitable compounds, fundamental theories have been tested during the past decades and many studies are still underway. Quantum phase transitions, possible coupling mechanisms to explain high-${T}_{C}$ superconductivity, ring exchange and orbital and spin currents, and the occurrence of Luttinger liquids and Bose-Einstein condensation are among the matters studied in this fascinating area of quantum systems. Here we add two values to this extensive list, which are the study of the spin anisotropy in spin-singlet ground-state compounds and the study of magnetic chirality, as measured by inelastic polarized neutron scattering techniques. To this end we have used the paramagnetic spin-singlet ground-state compound ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ and discussed in detail the scattering properties of the first excited state of the chain sublattice, a spin triplet. In-plane and out-of-plane magnetic fluctuations are measured to be anisotropic and further discussed in the light of the current hypothesis of spin-orbit coupling. We show that under appropriate conditions of magnetic field and neutron polarization, the trivial magnetic chirality selects only one of the Zeeman-split triplet states for scattering and erases the other one that possesses opposite helicity. Our analysis pertains to previous studies of dynamical magnetic chirality and chiral critical exponents, where the ground state is chiral itself, the so-called nontrivial dynamical magnetic chirality. As it turns out, both trivial and nontrivial dynamical magnetic chiralities have identical selection rules for inelastic polarized neutron scattering experiments and it is not at all evident that they can be distinguished in a paramagnetic compound.

Modified 1,4-hydroquinone ligands bridging CuII ions – Building blocks for a new class of quantum magnets

Abstract A series of low-dimensional quantum-spin systems, including isolated Cu II dimers, various coupled Cu II -dimer systems and a 1-D uniform S = 1/2 Heisenberg antiferromagnet has been synthesized. All materials are based on hydroquinone-derived linkers connecting Cu II ions carrying a spin of S = 1/2. Magnetic measurements covering wide ranges of temperature 0.06 K ≤ T ≤ 300 K and magnetic fields B ≤ 50 T reveal an antiferromagnetic coupling constant J of moderate strength for all systems. Electron-spin resonance measurements over wide frequency ranges have been used to determine the local coordination environment of the Cu II centers. The distinct magnetic properties of these materials along with their flexibility against chemical modifications make them excellent model systems for exploring fundamental aspects of quantum magnetism.

Cooperative Study by Neutron Scattering and NMR on Low Dimensional Quantum Spin System

We report the results of neutron scattering and nuclear magnetic resonance (NMR) measurements on the two-dimensional quantum spin system SrCu2(B03)2. The dispersion curve of the first excited state obtained by inelastic neutron scattering is almost flat. The Cu-NMR spectrum splits into four lines by the nuclear spin-spin coupling mediated by the electron spins of Cu ions which form dimers. These results are evidences of the characteristics suggested by theoretical studies. The Cu spectrum at 27.6, where the 1/8 plateau is observed in the magnetization curve, has a large number of peaks distributed over a wide frequency range. By comparing the NMR and theoretical results, the spin structure of the 1/8 plateau phase is determined. These results are good examples of the cooperative study by neutron scattering and NMR.

Two phase transitions in the low-dimensional quantum spin system TiOBr

Two phase transitions in the low-dimensional quantum spin system TiOBr

Quantum phase transitions in low-dimensional quantum spin systems with incommensurate magnetic structures

Several exactly solvable quantum spin models with incommensurate magnetic structures, which manifest quantum phase transitions between incommensurate and commensurate phases, are proposed. The ground-state and thermodynamic characteristics of these quantum spin antiferromagnetic models with the Dzyaloshinsky-Moriya antisymmetric exchange interaction and spin-frustrating next-nearest-neighbor, three-spin, and four-spin (ring exchange) interactions are exactly studied. We investigated the ground state phases of the considered models, as function of the magnetic anisotropy, Dzyaloshinsky-Moriya interaction, next-nearest-neighbor coupling constants, and external magnetic field. Several quantum phase transitions between magnetically incommensurate phases and between incommensurate and ferromagnetic phases are predicted, and the behavior of thermodynamic characteristics of those models at phase transitions is studied. We have shown that for models with chiral three-spin interactions the Dzyaloshinsky-Moriya coupling yields the onset of the weak ferromagnetism, similar to three-dimensional ordered antiferromagnets, but not present in other quantum spin chains with the antisymmetric exchange. Considered models appeared to be important for several quasi-one-dimensional spin systems, studied in recent experiments.