Chiral, nematic, and dimer states in quantum spin chains

Field-induced bound-state condensation and spin-nematic phase in SrCu2(BO3)2 revealed by neutron scattering up to 25.9 T

In quantum magnetic materials, ordered phases induced by an applied magnetic field can be described as the Bose-Einstein condensation (BEC) of magnon excitations. In the strongly frustrated system SrCu2(BO3)2, no clear magnon BEC could be observed, pointing to an alternative mechanism, but the high fields required to probe this physics have remained a barrier to detailed investigation. Here we exploit the first purpose-built high-field neutron scattering facility to measure the spin excitations of SrCu2(BO3)2 up to 25.9 T and use cylinder matrix-product-states (MPS) calculations to reproduce the experimental spectra with high accuracy. Multiple unconventional features point to a condensation of S = 2 bound states into a spin-nematic phase, including the gradients of the one-magnon branches and the persistence of a one-magnon spin gap. This gap reflects a direct analogy with superconductivity, suggesting that the spin-nematic phase in SrCu2(BO3)2 is best understood as a condensate of bosonic Cooper pairs.

Quantum phase transitions in skewed ladder systems

In this brief review, we introduce a new spin ladder system called skewed spin ladders and discuss the exotic quantum phases of this system. The spin ladders studied are the 5/7, 3/4 and 3/5 systems corresponding to alternately fused 5 and 7 membered rings; 3 and 4 membered rings; and 3 and 5 membered rings. These ladders show completely different behaviour as the Hamiltonian model parameter is changed. When the Hamiltonian parameter is increased the 5/7 ladder switches from an initial singlet ground state to progressively higher spin ground state and then to a reentrant singlet state before finally settling to the highest spin ground state whose spin equals the number of unit cells in the system. The 3/4 ladder goes from a singlet ground state to a high spin ground state with each unit cell contributing spin 1 to the state, as the model parameter is increased. The 3/5 ladder shows a singlet ground state for small parameters and high spin ground state for intermediate values of the parameter and for still higher parameters, a reentrant singlet ground state. They can also show interesting magnetization plateaus as illustrated by studies on a specific spin ladder.

Where is the Quantum Spin Nematic?

We provide strong evidence of the spin-nematic state in a paradigmatic ferro-antiferromagnetic J_{1}-J_{2} model using analytical and density-matrix renormalization group methods. In zero field, the attraction of spin-flip pairs leads to a first-order transition and no nematic state, while pair repulsion at larger J_{2} stabilizes the nematic phase in a narrow region near the pair-condensation field. A devil's staircase of multipair condensates is conjectured for weak pair attraction. A suppression of the spin-flip gap by many-body effects leads to an order-of-magnitude contraction of the nematic phase compared to naïve expectations. The proposed phase diagram should be broadly valid.

Machine learning approach to study quantum phase transitions of a frustrated one dimensional spin-1/2 system

Frustration-driven quantum fluctuation leads to many exotic phases in the ground state (GS) and the study of these quantum phase transitions is one of the most challenging areas of research in condensed matter physics. We study a frustrated HeisenbergJ1-J2model of spin-1/2 chain with nearest exchange interactionJ₁and next nearest exchange interactionJ₂using the principal component analysis (PCA) which is an unsupervised machine learning technique. In this method most probable spin configurations (MPSCs) of GS and first excited state (FES) for differentJ2/J1are used as the input in PCA to construct the covariance matrix. The 'quantified principal component'p1(J2/J1)of the largest eigenvalue of the covariance matrix is calculated and it is shown that the nature and variation ofp1(J2/J1)can accurately predict the phase transitions and degeneracies in the GS. Thep1(J2/J1)calculated from the MPSC of GS only exhibits the signature of degeneracies in the GS, whereas,p1(J2/J1)calculated from the MPSC of FES captures the gapless spin liquid (GSL)-dimer phase transition as well as all the degeneracies of the model system. We show that the jump inp1(J2/J1)of FES atJ2/J1≈0.241, indicates the GSL-dimer phase transition, whereas its kinks give the signature of the GS degeneracies. The scatter plot of the first two principal components of FES shows distinct band formation for different phases. The MPSCs are obtained by using an iterative variational method (IVM) which gives the approximate eigenvalues and eigenvectors.

High-Angular Momentum Excitations in Collinear Antiferromagnet FePS3

We report on magneto-optical studies of the quasi-two-dimensional van der Waals antiferromagnet FePS₃. Our measurements reveal an excitation that closely resembles the antiferromagnetic resonance mode typical of easy-axis antiferromagnets; nevertheless, it displays an unusual, four-times larger Zeeman splitting in an applied magnetic field. We identify this excitation with an |S_z| = 4 multipolar magnon─a single-ion 4-magnon bound state─that corresponds to a full reversal of a single magnetic moment of the Fe²⁺ ion. We argue that condensation of multipolar magnons in large-spin materials with a strong magnetic anisotropy can produce new exotic states.

Magnetic phase diagram of a spin-1/2 XXZ chain with modulated Dzyaloshinskii-Moriya interaction

We consider the ground-state phase diagram of a one-dimensional spin-1/2 XXZ chain with a spatially modulated Dzyaloshinskii-Moriya interaction in the presence of an alternating magnetic field applied along the z[over ̂] axis. The model is studied using the continuum-limit bosonization approach and the finite system exact numerical technique. In the absence of a magnetic field, the ground-state phase diagram of the model includes, besides the ferromagnetic and gapless Luttinger-liquid phases, two gapped phases: the composite (C1) phase characterized by the coexistence of long-range-ordered (LRO) alternating dimerization and spin chirality patterns, and the composite (C2) phase characterized by, in addition to the coexisting spin dimerization and alternating chirality patterns, the presence of LRO antiferromagnetic order. In the case of mentioned composite gapped phases, and in the case of a uniform magnetic field, the commensurate-incommensurate type quantum phase transitions from a gapful phase into a gapless phase have been identified and described using the bosonization treatment and finite chain exact diagonalization studies. The upper critical magnetic field corresponding to the transition into a fully polarized state has been also determined. It has been shown that the very presence of a staggered component of the magnetic field vapes the composite (C1) in favor of the composite gapped (C2) phase.

Quantum phases and thermodynamics of a frustrated spin-1/2 ladder with alternate Ising-Heisenberg rung interactions

We study a frustrated two-leg spin ladder with alternate isotropic Heisenberg and Ising rung exchange interactions, whereas, interactions along legs and diagonals are Ising-type. All the interactions in the ladder are anti-ferromagnetic in nature and induce frustration in the system. This model shows four interesting quantum phases: (i) stripe rung ferromagnetic (SRFM), (ii) stripe rung ferromagnetic with edge singlet (SRFM-E), (iii) anisotropic antiferromagnetic (AAFM), and (iv) stripe leg ferromagnetic (SLFM) phase. We construct a quantum phase diagram for this model and show that in stripe rung ferromagnet (SRFM), the same type of sublattice spins (either isotropicS-type or discrete anisotropicσ-type spins) are aligned in the same direction. Whereas, in anisotropic antiferromagnetic phase, bothSandσ-type of spins are anti-ferromagnetically aligned with each other, two nearestSspins along the rung form an anisotropic singlet bond whereas two nearestσspins form an Ising bond. In large Heisenberg rung exchange interaction limit, spins on each leg are ferromagnetically aligned, but spins on different legs are anti-ferromagnetically aligned. The thermodynamic quantities like specific heatC_v(T), magnetic susceptibilityχ(T) and thermal entropyS(T) are also calculated using the transfer matrix method for various phases. The magnetic gap in the SRFM and the SLFM can be noticed fromχ(T) andC_v(T) curves.

Crystal structure and magnetic properties of the magnetically isolated zigzag chain in KGaCu(PO4)2

Magnetism of any material depends on its crystal structure. However, two isostructural compounds such as MCuMoO4(OH) (M = Na, K) can have markedly different magnetic properties. Herein, we introduce a new method to describe the linkages between the O-atoms and their bridged Cu2+ ions in order to clearly illustrate the structure-magnetic property relationships. This new method can account for magnetic differences between the two isostructural MCuMoO4(OH) and is further confirmed by the rational design and development of a new compound KGaCu(PO4)2 with different linkages. The title compound crystalized in a space group of P21/c adopts a one-dimensional (1D) magnetically isolated S = 1/2 zigzag chain composed of elongated [CuO6] octahedra via sharing alternately equatorial and skew edges. O atoms at the skew edges bridge the equatorial and axial orbitals of neighbouring Cu2+ ions (denoted EOA), while those at the equatorial edges bridge the equatorial orbitals of Cu2+ ions (EOE). The nearest-neighbour (NN) magnetic coupling of Cu2+ ions with the EOA linkage at 2.821 Å in the title compound is negligible, whereas the NN magnetic coupling of Cu2+ ions with the EOE linkage at 2.974 Å is essential. Therefore, the zigzag chain containing alternating spin-exchange dimers and no-spin-exchange ones is similar in electronic configuration to the dimerization of the quasi-one-dimensional antiferromagnet. Magnetic investigation of analogous compounds with a 'trans-cis-trans-cis' configuration observed in the title compound may shed light on structural evolutions associated with spin-Peierls (SP) transition.

Dynamical Signatures of Quasiparticle Interactions in Quantum Spin Chains

We study the transverse dynamical susceptibility of an antiferromagnetic spin-1/2 chain in the presence of a longitudinal Zeeman field. In the low magnetization regime in the gapless phase, we show that the marginally irrelevant backscattering interaction between the spinons creates a nonzero gap between two branches of excitations at small momentum. We further demonstrate how this gap varies upon introducing a second neighbor antiferromagnetic interaction, vanishing in the limit of a noninteracting "spinon gas." In the high magnetization regime, as the Zeeman field approaches the saturation value, we uncover the appearance of two-magnon bound states in the transverse susceptibility. This bound state feature generalizes the one arising from string states in the Bethe ansatz solution of the integrable case. Our results are based on numerically accurate, unbiased matrix-product-state techniques as well as analytic approximations.

Magnon Pairs and Spin-Nematic Correlation in the Spin Seebeck Effect

Investigating exotic magnetic materials with spintronic techniques is effective at advancing magnetism as well as spintronics. In this work, we report unusual field-induced suppression of the spin Seebeck effect (SSE) in a quasi-one-dimensional frustrated spin-1/2 magnet LiCuVO_{4}, known to exhibit spin-nematic correlation in a wide range of external magnetic field B. The suppression takes place above |B|≳2  T in spite of the B-linear isothermal magnetization curves in the same B range. The result can be attributed to the growth of the spin-nematic correlation while increasing B. The correlation stabilizes magnon pairs carrying spin 2, thereby suppressing the interfacial spin injection of SSE by preventing the spin-1 exchange between single magnons and conduction electrons at the interface. This interpretation is supported by integrating thermodynamic measurements and theoretical analysis on the SSE.

Possible observation of quantum spin-nematic phase in a frustrated magnet

Water freezes into ice in winter and evaporates into vapor in summer. Scientifically, the transformations between solid, liquid, and gas are called phase transitions and can be classified through the changes in symmetry which occur in each case. A fourth phase of matter was discovered late in the 19th century: the liquid crystal nematic, in which rod- or disk-shaped molecules align like the atoms in a solid, while continuing to flow like a liquid. Here we report thermodynamic evidence of a quantum analog of the classical nematic phase, the quantum spin nematic (SN). In an SN, the spins of a quantum magnet select a common axis, like a nematic liquid crystal, while escaping conventional magnetic order. Our state-of-the-art thermal measurements in high pulsed magnetic fields up to 33 T on the copper mineral volborthite with spin 1/2 on a frustrated lattice provide thermodynamic evidence for SN order, half a century after the theoretical proposal [Blume M, Hsieh YY (1969) J Appl Phys 40:1249; Andreev AF, Grishchuk IA (1984) J Exp Theor Phys 97:467-475].

Signatures of a magnetic field-induced unconventional nematic liquid in the frustrated and anisotropic spin-chain cuprate LiCuSbO4

Modern theories of quantum magnetism predict exotic multipolar states in weakly interacting strongly frustrated spin-1/2 Heisenberg chains with ferromagnetic nearest neighbor (NN) inchain exchange in high magnetic fields. Experimentally these states remained elusive so far. Here we report strong indications of a magnetic field-induced nematic liquid arising above a field of ~13 T in the edge-sharing chain cuprate LiSbCuO₄ ≡ LiCuSbO₄. This interpretation is based on the observation of a field induced spin-gap in the measurements of the ⁷Li NMR spin relaxation rate T ₁^-1 as well as a contrasting field-dependent power-law behavior of T ₁^-1 vs. T and is further supported by static magnetization and ESR data. An underlying theoretical microscopic approach favoring a nematic scenario is based essentially on the NN XYZ exchange anisotropy within a model for frustrated spin-1/2 chains and is investigated by the DMRG technique. The employed exchange parameters are justified qualitatively by electronic structure calculations for LiCuSbO₄.

An efficient density matrix renormalization group algorithm for chains with periodic boundary condition

The Density Matrix Renormalization Group (DMRG) is a state-of-the-art numerical technique for a one dimensional quantum many-body system; but calculating accurate results for a system with Periodic Boundary Condition (PBC) from the conventional DMRG has been a challenging job from the inception of DMRG. The recent development of the Matrix Product State (MPS) algorithm gives a new approach to find accurate results for the one dimensional PBC system. The most efficient implementation of the MPS algorithm can scale as O($p \times m^3$), where $p$ can vary from 4 to $m^2$. In this paper, we propose a new DMRG algorithm, which is very similar to the conventional DMRG and gives comparable accuracy to that of MPS. The computation effort of the new algorithm goes as O($m^3$) and the conventional DMRG code can be easily modified for the new algorithm.Received: 2 August 2016,  Accepted: 12 October 2016; Edited by: K. Hallberg; DOI: http://dx.doi.org/10.4279/PIP.080006Cite as: D Dey, D Maiti, M Kumar, Papers in Physics 8, 080006 (2016)This paper, by D Dey, D Maiti, M Kumar, is licensed under the Creative Commons Attribution License 3.0. 

Quantum Dynamics of Ultracold Bose Polarons

We analyze the dynamics of Bose polarons in the vicinity of a Feshbach resonance between the impurity and host atoms. We compute the radio-frequency absorption spectra for the case when the initial state of the impurity is noninteracting and the final state is strongly interacting with the host atoms. We compare results of different theoretical approaches including a single excitation expansion, a self-consistent T-matrix method, and a time-dependent coherent state approach. Our analysis reveals sharp spectral features arising from metastable states with several Bogoliubov excitations bound to the impurity atom. This surprising result of the interplay of many-body and few-body Efimov type bound state physics can only be obtained by going beyond the commonly used Fröhlich model and including quasiparticle scattering processes. Close to the resonance we find that strong fluctuations lead to a broad, incoherent absorption spectrum where no quasiparticle peak can be assigned.

Frustration and chiral orderings in correlated electron systems

The term frustration refers to lattice systems whose ground state cannot simultaneously satisfy all the interactions. Frustration is an important property of correlated electron systems, which stems from the sign of loop products (similar to Wilson products) of interactions on a lattice. It was early recognized that geometric frustration can produce rather exotic physical behaviors, such as macroscopic ground state degeneracy and helimagnetism. The interest in frustrated systems was renewed two decades later in the context of spin glasses and the emergence of magnetic superstructures. In particular, Phil Anderson's proposal of a quantum spin liquid ground state for a two-dimensional lattice S  =  1/2 Heisenberg magnet generated a very active line of research that still continues. As a result of these early discoveries and conjectures, the study of frustrated models and materials exploded over the last two decades. Besides the large efforts triggered by the search of quantum spin liquids, it was also recognized that frustration plays a crucial role in a vast spectrum of physical phenomena arising from correlated electron materials. Here we review some of these phenomena with particular emphasis on the stabilization of chiral liquids and non-coplanar magnetic orderings. In particular, we focus on the ubiquitous interplay between magnetic and charge degrees of freedom in frustrated correlated electron systems and on the role of anisotropy. We demonstrate that these basic ingredients lead to exotic phenomena, such as, charge effects in Mott insulators, the stabilization of single magnetic vortices, as well as vortex and skyrmion crystals, and the emergence of different types of chiral liquids. In particular, these orderings appear more naturally in itinerant magnets with the potential of inducing a very large anomalous Hall effect.

Magnetic Vortex Induced by Nonmagnetic Impurity in Frustrated Magnets

We study the effect of a nonmagnetic impurity inserted in a two-dimensional frustrated ferromagnet above its saturation magnetic field H_{sat} for arbitrary spin S. We demonstrate that the ground state includes a magnetic vortex that is nucleated around the impurity over a finite range of magnetic field H_{sat}≤H≤H_{sat}^{I}. Upon approaching the quantum critical point at H=H_{sat}, the radius of the magnetic vortex diverges as the magnetic correlation length: ξ∝1/sqrt[H-H_{sat}]. These results are derived both for the lattice and in the continuum limit.

Quantum Lifshitz Field Theory of a Frustrated Ferromagnet

We propose a universal nonlinear sigma model field theory for one-dimensional frustrated ferromagnets, which applies in the vicinity of a "quantum Lifshitz point," at which the ferromagnetic state develops a spin wave instability. We investigate the phase diagram resulting from perturbations of the exchange and of magnetic field away from the Lifshitz point, and uncover a rich structure with two distinct regimes of different properties, depending upon the value of a marginal, dimensionless, parameter of the theory. In the regime relevant for one-dimensional systems with low spin, we find a metamagnetic transition line to a vector chiral phase. This line terminates in a critical end point, beyond which there is at least one multipolar or "spin nematic" phase. We show that the field theory is asymptotically exactly soluble near the Lifshitz point.

Unusual ordered phases of highly frustrated magnets: a review

We review ground states and excitations of a quantum antiferromagnet on triangular and other frustrated lattices. We pay special attention to the combined effects of magnetic field h, spatial anisotropy R and spin magnitude S. The focus of the review is on the novel collinear spin density wave and spin nematic states, which are characterized by fully gapped transverse spin excitations with S(z) = ± 1. We discuss extensively the R - h phase diagram of the antiferromagnet, both in the large-S semiclassical limit and the quantum S = 1/2 limit. When possible, we point out connections with experimental findings.

Anyonic liquids in nearly saturated spin chains

Most Heisenberg-like spin chains flow to a universal free-fermion fixed point near the magnetic-field induced saturation point. Here, we show that an exotic fixed point, characterized by two species of low-energy excitations with mutual anyonic statistics, may also emerge in such spin chains if the dispersion relation has two minima. By using bosonization, two-magnon exact calculations, and numerical density-matrix-renormalization-group calculations, we demonstrate the existence of this anyonic-liquid fixed point in an xxz spin chain with up to second-neighbor interactions. We also identify a range of microscopic parameters, which support this phase.

Quantum spin liquid in frustrated one-dimensional LiCuSbO4

A quantum magnet, LiCuSbO4, with chains of edge-sharing spin-1/2 CuO6 octahedra is reported. While short-range order is observed for T<10  K, no zero-field phase transition or spin freezing occurs down to 100 mK. Specific heat indicates a distinct high-field phase near the 12 T saturation field. Neutron scattering shows incommensurate spin correlations with q=(0.47±0.01)π/a and places an upper limit of 70  μeV on any spin gap. Exact diagonalization of 16-spin easy-plane spin-1/2 chains with competing ferro- and antiferromagnetic interactions (J1=-75  K, J2=34  K) accounts for the T>2  K data.

Magnetic frustration in a quantum spin chain: the case of linarite PbCuSO4(OH)2

We present a combined neutron diffraction and bulk thermodynamic study of the natural mineral linarite PbCuSO4(OH)2, this way establishing the nature of the ground-state magnetic order. An incommensurate magnetic ordering with a propagation vector k=(0,0.186,1/2) was found below T(N)=2.8 K in a zero magnetic field. The analysis of the neutron diffraction data yields an elliptical helical structure, where one component (0.638μ(B)) is in the monoclinic ac plane forming an angle with the a axis of 27(2)°, while the other component (0.833μ(B)) points along the b axis. From a detailed thermodynamic study of bulk linarite in magnetic fields up to 12 T, applied along the chain direction, a very rich magnetic phase diagram is established, with multiple field-induced phases, and possibly short-range-order effects occurring in high fields. Our data establish linarite as a model compound of the frustrated one-dimensional spin chain, with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. Long-range magnetic order is brought about by interchain coupling 1 order of magnitude smaller than the intrachain coupling.

Spin nematic order in multiple-spin exchange models on the triangular lattice

We figure out that the ground state of a multiple-spin exchange model applicable to thin films of solid {3}He possesses an octahedral spin nematic order. In the presence of a magnetic field, it is deformed into an antiferroquadrupolar order in the perpendicular spin plane, in which lattice Z{3} rotational symmetry is also broken. Furthermore, this system shows a narrow magnetization plateau at half, m/m{sat}=1/2, which resembles recent magnetization measurements [H. Nema et al., Phys. Rev. Lett. 102, 075301 (2009)].

Saturation field of frustrated chain cuprates: broad regions of predominant interchain coupling

A thermodynamic method to extract the interchain coupling (IC) of spatially anisotropic 2D or 3D spin-1/2 systems from their empirical saturation field H(s) (T=0) is proposed. Using modern theoretical methods we study how H(s) is affected by an antiferromagnetic (AFM) IC between frustrated chains described in the J(1)-J(2)-spin model with ferromagnetic 1st and AFM 2nd neighbor in-chain exchange. A complex 3D-phase diagram has been found. For Li(2)CuO(2) and Ca(2)Y(2)Cu(5)O(10), we show that H(s) is solely determined by the IC and predict H(s)≈61 T for the latter. With H(s)≈55 T from magnetization data one reads out a weak IC for Li(2)CuO(2) close to that obtained from inelastic neutron scattering.

Superfluidity and dimerization in a multilayered system of fermionic polar molecules

We consider a layered system of fermionic molecules with permanent dipole moments aligned perpendicular to the layers by an external field. The dipole interactions between fermions in adjacent layers are attractive and induce interlayer pairing. Because of the competition for pairing among adjacent layers, the mean-field ground state of the layered system is a dimerized superfluid, with pairing only between every other layer. We construct an effective Ising-XY lattice model that describes the interplay between dimerization and superfluid phase fluctuations. In addition to the dimerized superfluid ground state, and high-temperature normal state, at intermediate temperature, we find an unusual dimerized "pseudogap" state with only short-range phase coherence. We propose light-scattering experiments to detect dimerization.

Wigner crystal physics in quantum wires

The physics of interacting quantum wires has attracted a lot of attention recently. When the density of electrons in the wire is very low, the strong repulsion between electrons leads to the formation of a Wigner crystal. We review the rich spin and orbital properties of the Wigner crystal, in both the one-dimensional and the quasi-one-dimensional regimes. In the one-dimensional Wigner crystal the electron spins form an antiferromagnetic Heisenberg chain with exponentially small exchange coupling. In the presence of leads, the resulting inhomogeneity of the electron density causes a violation of spin-charge separation. As a consequence the spin degrees of freedom affect the conductance of the wire. Upon increasing the electron density, the Wigner crystal starts deviating from the strictly one-dimensional geometry, forming a zigzag structure instead. Spin interactions in this regime are dominated by ring exchanges, and the phase diagram of the resulting zigzag spin chain has a number of unpolarized phases as well as regions of complete and partial spin polarization. Finally we address the orbital properties in the vicinity of the transition from a one-dimensional to a quasi-one-dimensional state. Due to the locking between chains in the zigzag Wigner crystal, only one gapless mode exists. Manifestations of Wigner crystal physics at weak interactions are explored by studying the fate of the additional gapped low-energy mode as a function of interaction strength.

Octupolar order in the multiple spin exchange model on a triangular lattice

We show how a gapless spin liquid with hidden octupolar order arises in an applied magnetic field, in a model applicable to thin films of 3He with competing ferromagnetic and antiferromagnetic (cyclic) exchange interactions. Evidence is also presented for nematic--i.e., quadrupolar--correlations bordering on ferromagnetism in the absence of a magnetic field.

Nematic order in square lattice frustrated ferromagnets

We present a new scenario for the breakdown of ferromagnetic order in a two-dimensional quantum magnet with competing ferromagnetic and antiferromagnetic interactions. In this, dynamical effects lead to the formation of two-magnon bound states, which undergo Bose-Einstein condensation, giving rise to bond-centered nematic order. This scenario is explored in some detail for an extended Heisenberg model on a square lattice. In particular, we present numerical evidence confirming the existence of a state with d-wave nematic correlations but no long-range magnetic order, lying between the saturated ferromagnetic and collinear antiferromagnetic phases of the ferromagnetic model J1-J2. We argue by continuity of spectra that this phase is also present in a model with 4-spin cyclic exchange.