Antiferromagnetic Quantum Spin Chains Research Articles

Phase diagram of the topologically frustrated XY chain

Landau theory’s implicit assumption that microscopic details cannot affect the global phases has been challenged only recently in systems such as antiferromagnetic quantum spin chains with periodic boundary conditions. The new paradigm of topological frustration has been accordingly put forward. In this context, the quantum phases exhibit a dependence on the boundary conditions. In this work, we show that topological frustration modifies the zero temperature phase diagram of the XY chain in a transverse magnetic field by inducing new boundary quantum phase transitions. Here, by boundary quantum phase transitions we mean non-analyticities that are non-extensive in the number of particles. Such transitions are both of first and second order. Moreover, we come across the first case of second order boundary quantum phase transition characterized by a quartic dispersion relation. Our analytical results are supported by both analytical calculations and numerical investigations, and lay the foundation for understanding the phase diagram of frustrated model.

Magnetization process of antiferromagnetic quantum spin chains with the biquadratic exchange interaction

The magnetization processes of the S = 3/2 and S = 2 antiferromagnetic chains with the biquadratic interaction are investigated using the numerical diagonalization of the finite-size cluster. It is found that the system does not exhibit the spin nematic phase, which was predicted to occur for the S = 1 antiferromagnetic chain. Instead, the present analysis reveals that the quantum spin triatic and quatic liquid phases appear below the saturation magnetization for sufficiently large negative biquadratic interaction, for S = 3/2 and S = 2 chains, respectively. In addition it is also found that the magnetization jump up to the saturation magnetization appears for the small negative biquadratic interaction. The phase diagrams with respect to the negative biquadratic interaction and the magnetization are presented for the S = 3/2 and S = 2 antiferromagnetic chains.

Particle–hole symmetries in condensed matter

The term “particle–hole symmetry” is beset with conflicting meanings in contemporary physics. Conceived and written from a condensed-matter standpoint, the present paper aims to clarify and sharpen the terminology. In that vein, we propose to define the operation of “particle–hole conjugation” as the tautological algebra automorphism that simply swaps single-fermion creation and annihilation operators, and we construct its invariant lift to the Fock space. Particle–hole symmetries then arise for gapful or gapless free-fermion systems at half filling, as the concatenation of particle–hole conjugation with one or another involution that reverses the sign of the first-quantized Hamiltonian. We illustrate that construction principle with a series of examples including the Su–Schrieffer–Heeger model and the Kitaev–Majorana chain. For an enhanced perspective, we contrast particle–hole symmetries with the charge-conjugation symmetry of relativistic Dirac fermions. We go on to present two major applications in the realm of interacting electrons. For one, we offer a heuristic argument that the celebrated Haldane phase of antiferromagnetic quantum spin chains is adiabatically connected to a free-fermion topological phase protected by a particle–hole symmetry. For another, we review the recent proposal by Son [Phys. Rev. X 5, 031027 (2015)] for a particle–hole conjugation symmetric effective field theory of the half-filled lowest Landau level, and we comment on the emerging microscopic picture of the composite fermion.

Coexistence and Interaction of Spinons and Magnons in an Antiferromagnet with Alternating Antiferromagnetic and Ferromagnetic Quantum Spin Chains.

In conventional quasi-one-dimensional antiferromagnets with quantum spins, magnetic excitations are carried by either magnons or spinons in different energy regimes: they do not coexist independently, nor could they interact with each other. In this Letter, by combining inelastic neutron scattering, quantum MonteCarlo simulations, and random phase approximation calculations, we report the discovery and discuss the physics of the coexistence of magnons and spinons and their interactions in Botallackite-Cu_{2}(OH)_{3}Br. This is a unique quantum antiferromagnet consisting of alternating ferromagnetic and antiferromagnetic spin-1/2 chains with weak interchain couplings. Our study presents a new paradigm where one can study the interaction between two different types of magnetic quasiparticles: magnons and spinons.

Magnetization plateau of the S=2 antiferromagnetic Heisenberg chain with anisotropies

We investigate the $S=2$ antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using the numerical exact diagonalization of finite-size clusters and the level spectroscopy analysis. It is found that a magnetization plateau possibly appears at a half of the saturation magnetization for some suitable anisotropy parameters. The level spectroscopy analysis indicates that the 1/2 magnetization plateau is formed by two different mechanisms, depending on the anisotropy parameters. The phase diagram of the 1/2 plateau states and some typical magnetization curves are also presented. In addition the biquadratic interaction is revealed to enhance the plateau induced by the Haldane mechanism.

Experimental realization of long-distance entanglement between spins in antiferromagnetic quantum spin chains

Quantum communication relies on the ability to entangle quantum states. Experiments now show that this is possible in a bulk material, with unpaired spins at the ends of antiferromagnetic spin chains entangled over long distances.

Vector Chiral Phases in the Frustrated 2DXYModel and Quantum Spin Chains

The phase diagram of the frustrated 2D classical and 1D quantum XY models is calculated analytically. Four transitions are found: the vortex unbinding transitions triggered by strong fluctuations occur above and below the chiral transition temperature. Vortex interaction is short range on small and logarithmic on large scales. The chiral transition, though belonging to the Ising universality class by symmetry, has different critical exponents due to nonlocal interaction. In a narrow region close to the Lifshitz point a reentrant phase transition between paramagnetic and quasiferromagnetic phase appears. Applications to antiferromagnetic quantum spin chains and multiferroics are discussed.

Perfect Entanglement Transport in Quantum Spin Chain Systems

We propose a mechanism for perfect entanglement transport in anti-ferromagnetic (AFM) quantum spin chain systems with modulated exchange coupling and also for the modulation of on-site magnetic field. We use the principle of adiabatic quantum pumping process for entanglement transfer in the spin chain systems. We achieve the perfect entanglement transfer over an arbitrarily long distance and a better entanglement transport for longer AFM spin chain system than for the ferromagnetic one. We explain analytically and physically—why the entanglement hops in alternate sites. We find the condition for blocking of entanglement transport even in the perfect pumping situation. Our analytical solution interconnects quantum many body physics and quantum information science.

Effects of Two Energy Scales in Weakly Dimerized Antiferromagnetic Quantum Spin Chains

By means of thermal expansion and specific heat measurements on the high-pressure phase of (VO)(2)P(2)O(7), the effects of two energy scales of the weakly dimerized antiferromagnetic S=1/2 Heisenberg chain are explored. The low-energy scale, given by the spin gap Delta, is found to manifest itself in a pronounced thermal expansion anomaly. A quantitative analysis, employing the density-matrix renormalization-group approach for transfer matrices calculations, shows that this feature originates from changes in the magnetic entropy with respect to Delta, partial differentialS(m)/partial differentialDelta. This term, inaccessible by specific heat, is visible only in the weak-dimerization limit, where it reflects peculiarities of the excitation spectrum and its sensitivity to variations in Delta.

New polarization effect and collective excitation in S = 1/2 quasi-one-dimensional antiferromagnetic quantum spin chain

Anomalous polarization characteristics of magnetic resonance in CuGeO3 doped with 2% Co impurity are reported. For the Faraday geometry, this mode is damped for the microwave field B ω aligned along a certain crystallographic direction, showing that the character of magnetic oscillation differs from the standard spin precession. The observed resonance coexists with the ESR on Cu2+ chains; it is argued not to be caused by “impurity” EPR, as previously claimed, but to correspond to a previously unknown collective mode of magnetic oscillations in an S = 1/2 AF quantum spin chain.

Magnetic Properties of the Diamond Chain Compound Cu3(CO3)2(OH)2

Azurite (Cu 3 (CO 3 ) 2 (OH) 2 ) is a model substance of a diamond spin chain, one of frustrated antiferromagnetic quantum spin chains. The high field magnetization up to 60 T, magnetic susceptibility, magnetic entropy, muon spin relaxation and 1 H-NMR of azurite have been measured using single crystals. A distinct 1/3 magnetization plateau is confirmed to be present in the magnetization curve. Two resonance peaks of 1 H-NMR. were observed. By analyzing temperature dependencies of their hyperfine shift. we found two different local susceptibilities which correspond to susceptibility of dimer and monomer spins, respectively. New field induced phase transition was found to occur at a critical field where the magnetic plateau onsets. A short range magnetic ordering developed in a peculiar two-stage process, which was revealed by temperature dependence of the magnetic specific heat and susceptibility.

Phase diagrams and universality classes of random antiferromagnetic spin ladders

The random antiferromagnetic two-leg and zigzag spin-1/2 ladders are investigated using the real space renormalization group scheme and their complete phase diagrams are determined. We demonstrate that the first system belongs to the same universality class of the dimerized random spin-1/2 chain. The zigzag ladder, on the other hand, is in a random singlet phase at weak frustration and disorder. Otherwise, we give additional evidence that it belongs to the universality class of the random antiferromagnetic and ferromagnetic quantum spin chains, although the universal fixed point found in the latter system is never realized. We find, however, a new universal fixed point at intermediate disorder.

µSR Study of Cu Benzoate at Very Low Temperature – Existence or Nonexistence of Long Range Order in Coupled Chains –

Zero-, longitudinal- and transverse-field µSR experiments are performed for a linear chain antiferromagnet Cu benzoate, Cu(C 6 H 5 COO)·3H 2 O, and no long range order (LRO) is found down to 20 mK. The upper limit of the ratio of the Neel temperature to the exchange coupling, k B T N / J <0.002, is even better than that of Sr 2 CuO 3 , which is known as the best candidate of S =1/2 antiferromagnetic Heisenberg quantum spin chain. Significance of our findings is discussed in view of whether there is a non-zero critical coupling ratio necessary for LRO in coupled Heisenberg chains.

Anisotropic antiferromagnetic spin chains in a transverse field: Reentrant behavior of the staggered magnetization

We investigate one-dimensional $S=1/2$ and $S=1$ antiferromagnetic quantum-spin chains with easy-axis anisotropies in a transverse field. We calculate both the uniform magnetization and the staggered magnetization, using a variant of the density-matrix renormalization-group method. We find that the staggered magnetizations exhibit reentrant behavior as functions of the transverse field, where the competition between the classical N\'eel order and the quantum fluctuations plays an important role. We also discuss the critical behavior associated with the staggered magnetizations.

Random antiferromagnetic quantum spin chains: Exact results from scaling of rare regions

We study XY and dimerized XX spin-1/2 chains with random exchange couplings by analytical and numerical methods and scaling considerations. We extend previous investigations to dynamical properties, to surface quantities and operator profiles, and give a detailed analysis of the Griffiths phase. We present a phenomenological scaling theory of average quantities based on the scaling properties of rare regions, in which the distribution of the couplings follows a surviving random walk character. Using this theory we have obtained the complete set of critical decay exponents of the random XY and XX models, both in the volume and at the surface. The scaling results are confronted with numerical calculations based on a mapping to free fermions, which then lead to an exact correspondence with directed walks. The numerically calculated critical operator profiles on large finite systems (L<=512) are found to follow conformal predictions with the decay exponents of the phenomenological scaling theory. Dynamical correlations in the critical state are in average logarithmically slow and their distribution show multi-scaling character. In the Griffiths phase, which is an extended part of the off-critical region average autocorrelations have a power-law form with a non-universal decay exponent, which is analytically calculated. We note on extensions of our work to the random antiferromagnetic XXZ chain and to higher dimensions.

Interaction-round-a-face density-matrix renormalization-group method applied to rotational-invariant quantum spin chains

An interaction-round-a-face density-matrix renormalization-group (IRF-DMRG) method is developed for higher integer spin chain models which are rotational invariant. The expressions of the IRF weights associated with the nearest-neighbor spin-$S$ interaction ${\mathbf{S}}_{i}\ensuremath{\cdot}{\mathbf{S}}_{i+1}$ are explicitly derived. Using the IRF-DMRG with these IRF weights, the Haldane gaps $\ensuremath{\Delta}$ and the ground state energy densities ${e}_{0}$ for both $S=1$ and $S=2$ isotropic antiferromagnetic Heisenberg quantum spin chains are calculated by keeping up to only $m=90$ states.

Frustrated antiferromagnetic quantum spin chains for spin lengthS&gt;1

We investigate frustrated antiferromagnetic Heisenberg quantum spin chains at $T=0$ for $S=\frac{3}{2}$ and $S=2$ using the DMRG method. We localize disorder and Lifshitz points, confirming that quantum disorder points can be seen as quantum remnants of classical phase transitions. Both in the $S=\frac{3}{2}$ and the $S=2$ chain, we observe the disappearance of effectively free $S=\frac{1}{2}$ and $S=1$ end spins, respectively. The frustrated spin chain is therefore a suitable system for clearly showing the existence of free end spins ${S}^{\ensuremath{'}}=[S/2]$ also in half-integer antiferromagnetic spin chains with $S&gt;\frac{1}{2}.$ We suggest that the first-order transition found for $S=1$ in our previous work [A. K. Kolezhuk, R. Roth, and U. Schollw\"ock, Phys. Rev. Lett. 77, 5142 (1996); Phys. Rev. B 55, 8928 (1997)] is present in all frustrated spin chains with $S&gt;\frac{1}{2},$ characterized by the disappearance of effectively free end spins with ${S}^{\ensuremath{'}}=[S/2].$

On the second-neighbour correlator in 1D XXX quantum antiferromagnetic spin chain

We have calculated the energy per site for the ground state of the antiferromagnetic quantum spin chain with variable range exchange in the framework of the asymptotic Bethe ansatz. By expanding it in powers of , we have confirmed the value of the second-neighbour correlator for the model with nearest-neighbour exchange obtained earlier in the atomic limit of the Hubbard chain.

S=2 antiferromagnetic quantum spin chain.

We have investigated Haldane's conjecture for the S=2 antiferromagnetic quantum spin chain with nearest-neighbor exchange J. Using a density matrix renormalization group algorithm for chains up to L=350 spins, we find in the thermodynamic limit a finite gap of \ensuremath{\Delta}=0.085(5)J and a finite spin-spin correlation length \ensuremath{\xi}=49(1) lattice spacings. We have confirmed the gap value by a zero-temperature quantum Monte Carlo study. We show that the ground state has a hidden topological order that is revealed in a nonlocal string correlation function which saturates to a nonzero value in the thermodynamic limit. We investigate the behavior of the spin-2 chain under an easy-plane anisotropy D(${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$${)}^{2}$, D\ensuremath{\gtrsim}0, and find that the Haldane and the large-D phase are separated by an XY phase. The string correlation function vanishes only in the D\ensuremath{\rightarrow}\ensuremath{\infty} limit and does not distinguish between the Haldane phase and the perturbative large-D phase. An analysis of the transition mechanism and of the S=2 phase diagram in the presence of easy-plane and exchange anisotropy, markedly different from the S=1 phase diagram, allow us to conjecture how the classical limit is reached from increasing integer spins. \textcopyright{} 1996 The American Physical Society.

Edge states of integral quantum Hall states versus edge states of antiferromagnetic quantum spin chains.

Using the network model representation, it is shown that the edge states of finite-size integral quantum Hall liquid can be regarded as the edge states of an SU$(2N)$ open antiferromagnetic quantum spin chain in the $N \rightarrow 0$ limit. The structures of edge states in both cases of integer quantum Hall liquid and an SU$(2N)$ antiferromagnetic quantum spin chain are compared and the relations between them are pointed out. This correspondence is used to give qualitative arguments in favor of the recent results on two-dimensional electron systems coupled in layers with a large perpendicular magnetic field. In particular, it is shown that the absence of the localization in the two-dimensional chiral surface state of the integral quantum Hall liquid in the case of the finite-size coupled system can be explained by the absence of the gap in the excitation spectrum of an SU$(2N)$ ferromagnetic quantum spin chain in the $N \rightarrow 0$ limit.