Exact ground states with deconfined gapless excitations for the three-leg spin-1/2 tube

We consider a spin-1/2 tube (a three-leg ladder with periodic boundary conditions) with a Hamiltonian given by two projection operators-one on the triangles and the other on the square plaquettes on the side of the tube-that can be written in terms of Heisenberg and four-spin ring exchange interactions. We identify 3 phases: (i)?for strongly antiferromagnetic exchange on the triangles, an exact ground state with a gapped spectrum can be given as an alternation of spin and chirality singlet bonds between nearest triangles; (ii)?for ferromagnetic exchange on the triangles, we recover the phase of the spin-3/2 Heisenberg chain; (iii)?between these two phases, a gapless incommensurate phase exists. We construct an exact ground state with two deconfined domain walls and a gapless excitation spectrum at the quantum phase transition point between the incommensurate and dimerized phases.     

Ising phases of Heisenberg ladders in a magnetic field

We show that Dzyaloshinskii-Moriya (DM) interactions can substantially modify the phase diagram of spin-1/2 Heisenberg ladders in a magnetic field provided they compete with exchange. For nonfrustrated ladders, they induce a local magnetization along the DM vector that turns the gapless intermediate phase into an Ising phase with broken translational symmetry, while for frustrated ladders, they extend the Ising order of the half-integer plateau to the surrounding gapless phases of the purely Heisenberg case. Implications for experimental ladder and dimer systems are discussed.     

Magnetic phase diagram of the dimerized spin S = 1/2 ladder

The ground-state magnetic phase diagram of a spin S=1/2 two-leg ladder with alternating rung exchange J_⊥(n)=J_⊥[1 + (-1)ⁿ δ] is studied using the analytical and numerical approaches. In the limit where the rung exchange is dominant, we have mapped the model onto the effective quantum sine-Gordon model with topological term and identified two quantum phase transitions at magnetization equal to the half of saturation value from a gapped to the gapless regime. These quantum transitions belong to the universality class of the commensurate-incommensurate phase transition. We have also shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. We also present a detailed numerical analysis of the low energy excitation spectrum and the ground state magnetic phase diagram of the ladder with rung-exchange alternation using Lanczos method of numerical diagonalizations for ladders with number of sites up to N = 28. We have calculated numerically the magnetic field dependence of the low-energy excitation spectrum, magnetization and the on-rung spin-spin correlation function. We have also calculated the width of the magnetization plateau and show that it scales as δ^ν, where critical exponent varies from ν = 0.87±0.01 in the case of a ladder with isotropic antiferromagnetic legs to ν = 1.82±0.01 in the case of ladder with ferromagnetic legs. Obtained numerical results are in an complete agreement with estimations made within the continuum-limit approach.     

High-pressure sequence of Ba3NiSb2O9 structural phases: new S = 1 quantum spin liquids based on Ni2+

Two new gapless quantum spin-liquid candidates with S = 1 (Ni(2+)) moments: the 6H-B phase of Ba(3)NiSb(2)O(9) with a Ni(2+)-triangular lattice and the 3C phase with a Ni(2/3)Sb(1/3)-three-dimensional edge-shared tetrahedral lattice were obtained under high pressure. Both compounds show no magnetic order down to 0.35 K despite Curie-Weiss temperatures θ(CW) of -75.5 (6H-B) and -182.5 K (3C), respectively. Below ~25 K, the magnetic susceptibility of the 6H-B phase saturates to a constant value χ(0) = 0.013 emu/mol, which is followed below 7 K by a linear-temperature-dependent magnetic specific heat (C(M)) displaying a giant coefficient γ = 168 mJ/mol K(2). Both observations suggest the development of a Fermi-liquid-like ground state. For the 3C phase, the C(M) perpendicular T(2) behavior indicates a unique S = 1, 3D quantum spin-liquid ground state.     

Thermodynamics of a dilute XX chain in a field

Gapless phases in ground states of low-dimensional quantum spin systems are rather ubiquitous. Their peculiarity is a remarkable sensitivity to external perturbations due to permanent criticality of such phases manifested by a slow (power-low) decay of pair correlations and the divergence of the corresponding susceptibility. A strong influence of various defects on the properties of the system in such a phase can then be expected. Here, we consider the influence of vacancies on the thermodynamics of the simplest quantum model with a gapless phase, the isotropic spin-1/2 XX chain. The existence of the exact solution of this model gives a unique opportunity to describe in detail the dramatic effect of dilution on the gapless phase—the appearance of an infinite series of quantum phase transitions resulting from level crossing under the variation of a longitudinal magnetic field. We calculate the jumps in the field dependences of the ground-state longitudinal magnetization, susceptibility, entropy, and specific heat appearing at these transitions and show that they result in a highly nonlinear temperature dependence of these parameters at low T. Also, the effect of enhancement of the magnetization and longitudinal correlations in the dilute chain is established. The changes of the pair spin correlators under dilution are also analyzed. The universality of the mechanism of the quantum transition generation suggests that similar effects of dilution can also be expected in gapless phases of other low-dimensional quantum spin systems.     

Two-dimensional quantum-spin-1/2 XXZ magnet in zero magnetic field: Global thermodynamics from renormalisation group theory

Phase diagram, critical properties and thermodynamic functions of the two-dimensional field-free quantum-spin-1/2 XXZ model has been calculated globally using a numerical renormalisation group theory. The nearest-neighbour spin-spin correlations and entanglement properties, as well as internal energy and specific heat are calculated globally at all temperatures for the whole range of exchange interaction anisotropy, from XY limit to Ising limits, for both antiferromagnetic and ferromagnetic cases. We show that there exists long-range (quasi-long-range) order at low-temperatures, and the low-lying excitations are gapped (gapless) in the Ising-like easy-axis (XY-like easy-plane) regime. Besides, we identify quantum phase transitions at zero-temperature.     

Gapless color-flavor-locked quark matter

In neutral cold quark matter that is so dense that the strange quark mass Ms is unimportant, all three quark flavors pair in a color-flavor locked (CFL) pattern, and all nine fermionic quasiparticles have a gap Delta (or 2Delta). We argue that, as the density decreases (or Ms increases), there is a quantum phase transition (at M(2s/mu approximately 2Delta) to a new "gapless CFL phase" in which only seven quasiparticles have a gap. There is still an unbroken U(1)(Q) gluon/photon, but, unlike CFL, gapless CFL is a Q conductor with gapless (charged) quasiquarks and a nonzero electron density at zero temperature, so its low energy effective theory and astrophysical properties are qualitatively new. At the transition, the dispersion relations of both gapless quasiparticles are quadratic, but for larger M2s/mu, one becomes conventionally linear while the other remains quadratic, up to tiny corrections.     

Exotic gapless mott insulators of bosons on multileg ladders

We present evidence for an exotic gapless insulating phase of hard-core bosons on multileg ladders with a density commensurate with the number of legs. In particular, we study in detail a model of bosons moving with direct hopping and frustrating ring exchange on a 3-leg ladder at ν=1/3 filling. For sufficiently large ring exchange, the system is insulating along the ladder but has two gapless modes and power law transverse density correlations at incommensurate wave vectors. We propose a determinantal wave function for this phase and find excellent comparison between variational Monte Carlo and density matrix renormalization group calculations on the model Hamiltonian, thus providing strong evidence for the existence of this exotic phase. Finally, we discuss extensions of our results to other N-leg systems and to N-layer two-dimensional structures.     

Dynamical quantum phase transition in XY chains with the Dzyaloshinskii-Moriya and XZY-YZX three-site interactions

We study the dynamical quantum phase transitions (DQPTs) in the $XY$ chains with the Dzyaloshinskii-Moriya interaction and the $XZY$-$YZX$ type of three-site interaction after a sudden quench. Both the models can be mapped to the spinless free fermion models by the Jordan-Wigner and Bogoliubov transformations with the form $H=\sum_{k}ǎrepsilon_{k}(\eta^{†}_{k}\eta_{k}-\frac{1}{2})$, where the quasiparticle excitation spectra $ǎrepsilon_{k}$ may be smaller than 0 for some $k$ and are asymmetrical ($ǎrepsilon_{k}\neqǎrepsilon_{-k}$). It is found that the factors of Loschmidt echo equal 1 for some $k$ corresponding to the quasiparticle excitation spectra of the pre-quench Hamiltonian satisfying $ǎrepsilon_{k}\cdotǎrepsilon_{-k}<0$, when the quench is from the gapless phase. By considering the quench from different ground states, we obtain the conditions for the occurrence of DQPTs for the general $XY$ chains with gapless phase, and find that the DQPTs may not occur in the quench across the quantum phase transitions regardless of whether the quench is from the gapless phase to gapped phase or from the gapped phase to gapless phase. This is different from the DQPTs in the case of quench from the gapped phase to gapped phase, in which the DQPTs will always appear. Moreover, we analyze the different reasons for the absence of DQPTs in the quench from the gapless phase and the gapped phase. The conclusion can also be extended to the general quantum spin chains.     

Phase Diagram of the Spin-1/2 Heisenberg Alternating Chain in a Magnetic Field *

By using the infinite time-evolving block decimation, we study quantum fidelity and entanglemententropy in the spin-1/2 Heisenberg alternating chain under an external magnetic field .The effects of the magnetic field on the fidelity are investigated, and its relation with the quantum hase transition (QPT) is analyzed. The phase diagram of the model is given accordingly, which supports the Haldane phase, the singlet-dimer phase, the Luttinger liquid phase and the paramagnetic phase. The scaling of entanglement entropy in the gapless Luttinger liquid phase is studied, and the central charge $c=1$ is obtained. We also study the relationship between the quantum coherence, string order parameter and QPTs. Results obtained from these quantum information observations are consistent with the previous reports.     

Thermodynamic properties of the spin-1/2 antiferromagnetic ladder under magnetic field

Specific heat (C_V) measurements in the spin-1/2 Cu₂(C₂H₁₂N₂)₂Cl₄ system under a magnetic field up to H =8.25 T are reported and compared to the results of numerical calculations based on the 2-leg antiferromagnetic Heisenberg ladder. While the temperature dependences of both the susceptibility and the low-field specific heat are accurately reproduced by this model, deviations are observed above the critical field H_C1 at which the spin gap closes. In this Quantum High Field phase, the contribution of the low-energy quantum fluctuations are stronger than in the Heisenberg ladder model. We argue that this enhancement can be attributed to dynamical lattice fluctuations. Finally, we show that such a Heisenberg ladder, for H > H C1, is unstable, when coupled to the 3D lattice, against a lattice distortion. These results provide an alternative explanation for the observed low temperature ( K-0.8 K) phase (previously interpreted as a 3D magnetic ordering) as a new type of incommensurate gapped state. Received: 23 July 1998 / Accepted: 24 August 1998     

两腿XXZ自旋梯子模型的量子相变与量子临界现象

对于无限大尺寸两腿自旋1/2的XXZ自旋梯子模型,通过运用基于随机行走的张量网络(TN)算法数值模拟出基态波函数,首次尝试研究自旋梯子模型的约化保真度、普适序参量、纠缠熵等物理观测量,并系统研究基态保真度的三维挤点与二维分叉、约化保真度的分叉、局域序参量、普适序参量、纠缠熵和量子相变之间存在的关联关系.基于张量网络表示的算法在任意随机选择初始状态时,可以得到两腿XXZ量子自旋梯子系统简并的对称破缺基态波函数,该基态波函数是由于Z2对称破缺引起的.本文期望所提供的方法可为进一步研究凝聚态物质中热力学极限下的强关联电子量子晶格自旋梯子系统的量子相变和量子临界现象提供一种更有效的强大的工具.     

Magnetic properties of the spin S = 1/2 Heisenberg chain with hexamer modulation of exchange

We consider the spin-1/2 Heisenberg chain with alternating spin exchange in the presence of additional modulation of exchange on odd bonds with period 3. We study the ground state magnetic phase diagram of this hexamer spin chain in the limit of very strong antiferromagnetic (AF) exchange on odd bonds using the numerical Lanczos method and bosonization approach. In the limit of strong magnetic field commensurate with the dominating AF exchange, the model is mapped onto an effective XXZ Heisenberg chain in the presence of uniform and spatially modulated fields, which is studied using the standard continuum-limit bosonization approach. In the absence of additional hexamer modulation, the model undergoes a quantum phase transition from a gapped phase into the only one gapless Lüttinger liquid (LL) phase by increasing the magnetic field. In the presence of hexamer modulation, two new gapped phases are identified in the ground state at magnetization equal to [Formula: see text] and [Formula: see text] of the saturation value. These phases reveal themselves also in the magnetization curve as plateaus at corresponding values of magnetization. As a result, the magnetic phase diagram of the hexamer chain shows seven different quantum phases, four gapped and three gapless, and the system is characterized by six critical fields which mark quantum phase transitions between the ordered gapped and the LL gapless phases.     

Energy gap of spin nanotube

Recently some quantum spin systems on tube lattices, so-called spin nanotubes, have been synthesized. They are expected to be interesting low-dimensional systems like the carbon nanotubes. As a first step of theoretical study on the spin nanotube, we investigate the three-leg spin tube, which is the simplest one, using numerical analyses of finite clusters and a finite-size scaling technique. The spin gap, which is one of the most interesting quantities reflecting the macroscopic quantum effect, was revealed to be open for any finite rung exchange couplings, in contrast to the three-leg spin ladder system which is gapless. We also found a quantum phase transition caused by an asymmetric rung interaction. When one of the three rung coupling constants is changed, the spin gap vanishes very rapidly.     

具有Dzyaloshinskii-Moriya相互作用的XY模型的量子相干性

研究了具有Dzyaloshinskii-Moriya(DM)相互作用的一维横场XY自旋链的量子相变和量子相干性.采用约旦-维格纳变换严格求解了哈密顿量,并描绘了体系的关联函数和相图,相图包含反铁磁相、顺磁相和螺旋相.利用相对熵和Jensen-Shannon熵讨论了XY模型的量子相干性.研究发现,相对熵与Jensen-Shannon熵所表现的行为都可以很好地表征该模型的量子相变.非螺旋相中量子相干性不依赖DM相互作用,而在螺旋相DM相互作用对量子相干性有显著影响.此外,指出了在带有DM相互作用的这一类反射对称破缺体系中关联函数计算的常见问题.     

Field-induced freezing of a quantum spin liquid on the kagome lattice

We report (17)O NMR measurements in the S=1/2 (Cu(2+)) kagome antiferromagnet Herbertsmithite ZnCu(3)(OH)(6)Cl(2) down to 45 mK in magnetic fields ranging from 2 to 12 T. While Herbertsmithite displays a gapless spin-liquid behavior in zero field, we uncover an instability toward a spin-solid phase at sub-Kelvin temperature induced by an applied magnetic field. The latter phase shows largely suppressed moments ?0.1 μ(B) and gapped excitations. The H-T phase diagram suggests the existence of a quantum critical point at the small but finite magnetic field μ(0)H(c)=1.55(25) T. We discuss this finding in light of the perturbative Dzyaloshinskii-Moriya interaction which was theoretically proposed to sustain a quantum critical regime for the quantum kagome Heisenberg antiferromagnet model.     

Specific heat study of an S = 1/2 alternating Heisenberg chain system: F5PNN in a magnetic field

We have measured the specific heat of an S = 1/2 antiferromagnetic alternating Heisenberg chain pentafulorophenyl nitronyl nitroxide in magnetic fields up to H > H(C2). This compound has a field-induced magnetic ordered (FIMO) phase between H(C1) and H(C2). Characteristic behaviors are observed depending on the magnetic field up to above H(C2) outside of the H-T boundary for the FIMO. The temperature and field dependence of the specific heat are qualitatively in good agreement with the theoretical calculation on an S = 1/2 two-leg ladder [Wang et al., Phys. Rev. Lett. 84, 5399 (2000)]]. This agreement suggests that the observed behaviors are related with the low-energy excitation in the Tomonaga-Luttinger liquid.     

Ferrimagnetism and metal–insulator transition in an organic polymer chain

The ferrimagnetism and quantum phase transition of a bipartite lozenge periodic Anderson-like organic polymer, in which the localized f electrons hybridize with the odd site conduction orbitals, are investigated by means of Green＇s function theory. The ground state turns out to be gapless ferrimagnetism. At a finite temperature, the ferrimagnetic-to- paramagnetic phase transition takes place. The Kondo screenings and Ruderman-Kittel-Kasuya-Yosida （RKKY） inter- action can reduce and increase the transition temperature, respectively. Two Kondo screenings compete with each other, giving rise to the localized f electron spin screened antiferromagnetically. Accordingly, in a magnetic field, all spins are aligned along the chain easily, which is associated with metal-insulator transition. Furthermore, in a temperature-field plane, we reveal the gapless and spin polarized phases, which are characterized by susceptibility and specific heat, and whose behaviours are determined by the competition between the up-spin and down-spin hole excitations.     

Quantum decoupling transition in a one-dimensional Feshbach-resonant superfluid

We study a one-dimensional gas of fermionic atoms interacting via an s-wave molecular Feshbach resonance. At low energies the system is characterized by two Josephson-coupled Luttinger liquids, corresponding to paired atomic and molecular superfluids. We show that, in contrast to higher dimensions, the system exhibits a quantum phase transition from a phase in which the two superfluids are locked together to one in which, at low energies, quantum fluctuations suppress the Feshbach resonance (Josephson) coupling, effectively decoupling the molecular and atomic superfluids. Experimental signatures of this quantum transition include the appearance of an out-of-phase gapless mode (in addition to the standard gapless in-phase mode) in the spectrum of the decoupled superfluid phase and a discontinuous change in the molecular momentum distribution function.     

Dissipationless transport in low-density bilayer systems

In a bilayer electronic system the layer index may be viewed as the z component of an isospin- 1 / 2. An XY isospin-ordered ferromagnetic phase was observed in quantum Hall systems and is predicted to exist at zero magnetic field at low density. This phase is a superfluid for opposite currents in the two layers. At B = 0 the system is gapless but superfluidity is not destroyed by weak disorder. In the quantum Hall case, weak disorder generates a random gauge field which probably does not destroy superfluidity. Experimental signatures include Coulomb drag and collective mode measurements.