Quantum Spin Chains Research Articles

Encoding Information on the Excited State of a Molecular Spin Chain

AbstractThe quantum states of nano‐objects can drive electrical transport properties across lateral and local‐probe junctions. This raises the prospect, in a solid‐state device, of electrically encoding information at the quantum level using spin‐flip excitations between electron spins. However, this electronic state has no defined magnetic orientation and is short‐lived. Using a novel vertical nanojunction process, these limitations are overcome and this steady‐state capability is experimentally demonstrated in solid‐state spintronic devices. The excited quantum state of a spin chain formed by Co phthalocyanine molecules coupled to a ferromagnetic electrode constitutes a distinct magnetic unit endowed with a coercive field. This generates a specific steady‐state magnetoresistance trace that is tied to the spin‐flip conductance channel, and is opposite in sign to the ground state magnetoresistance term, as expected from spin excitation transition rules. The experimental 5.9 meV thermal energy barrier between the ground and excited spin states is confirmed by density functional theory, in line with macrospin phenomenological modeling of magnetotransport results. This low‐voltage control over a spin chain's quantum state and spintronic contribution lay a path for transmitting spin wave‐encoded information across molecular layers in devices. It should also stimulate quantum prospects for the antiferromagnetic spintronics and oxides electronics communities.

Mapping current and activity fluctuations in exclusion processes: consequences and open questions

Considering the large deviations of activity and current in the Asymmetric Simple Exclusion Process (ASEP), we show that there exists a non-trivial correspondence between the joint scaled cumulant generating functions of activity and current of two ASEPs with different parameters. This mapping is obtained by applying a similarity transform on the deformed Markov matrix of the source model in order to obtain the deformed Markov matrix of the target model. We first derive this correspondence for periodic boundary conditions, and show in the diffusive scaling limit (corresponding to the Weakly Asymmetric Simple Exclusion Processes, or WASEP) how the mapping is expressed in the language of Macroscopic Fluctuation Theory (MFT). As an interesting specific case, we map the large deviations of current in the ASEP to the large deviations of activity in the SSEP, thereby uncovering a regime of Kardar--Parisi--Zhang in the distribution of activity in the SSEP. At large activity, particle configurations exhibit hyperuniformity [Jack et al., PRL 114, 060601 (2015)]. Using results from quantum spin chain theory, we characterize the hyperuniform regime by evaluating the small wavenumber asymptotic behavior of the structure factor at half-filling. Conversely, we formulate from the MFT results a conjecture for a correlation function in spin chains at any fixed total magnetization (in the thermodynamic limit). In addition, we generalize the mapping to the case of two open ASEPs with boundary reservoirs, and we apply it in the WASEP limit in the MFT formalism. This mapping also allows us to find a symmetry-breaking dynamical phase transition (DPT) in the WASEP conditioned by activity, from the prior knowledge of a DPT in the WASEP conditioned by the current.

Exact solutions of the Cn quantum spin chain

We study the exact solutions of quantum integrable model associated with the Cn Lie algebra, with either a periodic or an open one with off-diagonal boundary reflections, by generalizing the nested off-diagonal Bethe ansatz method. Taking the C3 as an example we demonstrate how the generalized method works. We give the fusion structures of the model and provide a way to close fusion processes. Based on the resulted operator product identities among fused transfer matrices and some necessary additional constraints such as asymptotic behaviors and relations at some special points, we obtain the eigenvalues of transfer matrices and parameterize them as homogeneous T−Q relations in the periodic case or inhomogeneous ones in the open case. We also give the exact solutions of the Cn model with an off-diagonal open boundary condition. The method and results in this paper can be generalized to other high rank integrable models associated with other Lie algebras.

A classification of pure states on quantum spin chains satisfying the split property with on-site finite group symmetries

We consider a set S P G ( A ) SPG(\mathcal {A}) of pure split states on a quantum spin chain A \mathcal {A} which are invariant under the on-site action τ \tau of a finite group G G . For each element ω \omega in S P G ( A ) SPG(\mathcal {A}) we can associate a second cohomology class c ω , R c_{\omega ,R} of G G . We consider a classification of S P G ( A ) SPG(\mathcal {A}) whose criterion is given as follows: ω 0 \omega _{0} and ω 1 \omega _{1} in S P G ( A ) SPG(\mathcal {A}) are equivalent if there are automorphisms Ξ R \Xi _{R} , Ξ L \Xi _L on A R \mathcal {A}_{R} , A L \mathcal {A}_{L} (right and left half infinite chains) preserving the symmetry τ \tau , such that ω 1 \omega _{1} and ω 0 ∘ ( Ξ L ⊗ Ξ R ) \omega _{0}\circ \left ( \Xi _{L}\otimes \Xi _{R}\right ) are quasi-equivalent. It means that we can move ω 0 \omega _{0} close to ω 1 \omega _{1} without changing the entanglement nor breaking the symmetry. We show that the second cohomology class c ω , R c_{\omega ,R} is the complete invariant of this classification.

Studying Viral Populations with Tools from Quantum Spin Chains

We study Eigen's model of quasi-species, characterized by sequences that replicate with a specified fitness and mutate independently at single sites. The evolution of the population vector in time is then closely related to that of quantum spins in imaginary time. We employ multiple perspectives and tools from interacting quantum systems to examine growth and collapse of realistic viral populations, specifically certain HIV proteins. All approaches used, including the simplest perturbation theory, give consistent results.

The action of the Virasoro algebra in quantum spin chains. Part I. The non-rational case

We investigate the action of discretized Virasoro generators, built out of generators of the lattice Temperley-Lieb algebra (“Koo-Saleur generators” [1]), in the critical XXZ quantum spin chain. We explore the structure of the continuum-limit Virasoro modules at generic central charge for the XXZ vertex model, paralleling [2] for the loop model. We find again indecomposable modules, but this time not logarithmic ones. The limit of the Temperley-Lieb modules Wj,1 for j ≠ 0 contains pairs of “conjugate states” with conformal weights (hr,s, hr,−s) and (hr,−s, hr,s) that give rise to dual structures: Verma or co-Verma modules. The limit of {W}_{0,{mathfrak{q}}^{pm 2}} contains diagonal fields (hr,1, hr,1) and gives rise to either only Verma or only co-Verma modules, depending on the sign of the exponent in {mathfrak{q}}^{pm 2} . In order to obtain matrix elements of Koo-Saleur generators at large system size N we use Bethe ansatz and Quantum Inverse Scattering methods, computing the form factors for relevant combinations of three neighbouring spin operators. Relations between form factors ensure that the above duality exists already at the lattice level. We also study in which sense Koo-Saleur generators converge to Virasoro generators. We consider convergence in the weak sense, investigating whether the commutator of limits is the same as the limit of the commutator? We find that it coincides only up to the central term. As a side result we compute the ground-state expectation value of two neighbouring Temperley-Lieb generators in the XXZ spin chain.

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.

Real-time scattering of interacting quasiparticles in quantum spin chains

We develop a method based on tensor networks to create localized single particle excitations on top of strongly-correlated quantum spin chains. In analogy to the problem of creating localized Wannier modes, this is achieved by optimizing the gauge freedom of momentum excitations on top of matrix product states. The corresponding wavepackets propagate almost dispersionless. The time-dependent variational principle is used to scatter two such wavepackets, and we extract the phase shift from the collision data. We also study reflection and transmission coefficients of a wavepacket impinging on an impurity.

Hydrodynamics in lattice models with continuous non-Abelian symmetries

We develop a systematic effective field theory of hydrodynamics for many-body systems on the lattice with global continuous non-Abelian symmetries. Models with continuous non-Abelian symmetries are ubiquitous in physics, arising in diverse settings ranging from hot nuclear matter to cold atomic gases and quantum spin chains. In every dimension and for every flavor symmetry group, the low energy theory is a set of coupled noisy diffusion equations. Independence of the physics on the choice of canonical or microcanonical ensemble is manifest in our hydrodynamic expansion, even though the ensemble choice causes an apparent shift in quasinormal mode spectra. We use our formalism to explain why flavor symmetry is qualitatively different from hydrodynamics with other non-Abelian conservation laws, including angular momentum and charge multipoles.As a significant application of our framework, we study spin and energy diffusion in classical one-dimensional SU(2)-invariant spin chains, including the Heisenberg model along with multiple generalizations. We argue based on both numerical simulations and our effective field theory framework that non-integrable spin chains on a lattice exhibit conventional spin diffusion, in contrast to some recent predictions that diffusion constants grow logarithmically at late times. We show that the apparent enhancement of diffusion is due to slow equilibration caused by (non-Abelian) hydrodynamic fluctuations.

Unraveling the Nature of Exotic Phase Transitions in Quantum Spin Chains

Researchers from Kyushu University have succeeded in identifying a quantum field theory that describes the unusual phase transition in a quantum spin chain composed of spin-1 particles. This was ac...

Slow Propagation in Some Disordered Quantum Spin Chains

We introduce the notion of transmission time to study the dynamics of disordered quantum spin chains and prove results relating its behavior to many-body localization properties. We also study two versions of the so-called Local Integrals of Motion (LIOM) representation of spin chain Hamiltonians and their relation to dynamical many-body localization. We prove that uniform-in-time dynamical localization expressed by a zero-velocity Lieb-Robinson bound implies the existence of a LIOM representation of the dynamics as well as a weak converse of this statement. We also prove that for a class of spin chains satisfying a form of exponential dynamical localization, sparse perturbations result in a dynamics in which transmission times diverge at least as a power law of distance, with a power for which we provide lower bound that diverges with increasing sparseness of the perturbation.

Integrable quantum spin chains with free fermionic and parafermionic spectrum

We present a general study of the large family of exact integrable quantum chains with multispin interactions introduced recently in \cite{AP2020}. The exact integrability follows from the algebraic properties of the energy density operators defining the quantum chains. The Hamiltonians are characterized by a parameter $p=1,2,\dots$ related to the number of interacting spins in the multispin interaction. In the general case the quantum spins are of infinite dimension. In special cases, characterized by the parameter $N=2,3,\ldots$, the quantum chains describe the dynamics of $Z(N)$ quantum spin chains. The simplest case $p=1$ corresponds to the free fermionic quantum Ising chain ($N=2$) or the $Z(N)$ free parafermionic quantum chain. The eigenenergies of the quantum chains are given in terms of the roots of special polynomials, and for general values of $p$ the quantum chains are characterized by a free fermionic ($N=2$) or free parafermionic ($N>2$) eigenspectrum. The models have a special critical point when all coupling constants are equal. At this point the ground-state energy is exactly calculated in the bulk limit, and our analytical and numerical analyses indicate that the models belong to universality classes of critical behavior with dynamical critical exponent $z = (p+1)/N$ and specific-heat exponent $\alpha = \max\{0,1-(p+1)/N\}$.

Quantum hydrodynamics of spin winding

An easy-plane spin winding in a quantum spin chain can be treated as a transport quantity, which propagates along the chain but has a finite lifetime due to phase slips. In a hydrodynamic formulation for the winding dynamics, the quantum continuity equation acquires a source term due to the transverse vorticity flow. The latter reflects the phase slips and generally compromises the global conservation law. A linear-response formalism for the nonlocal winding transport then reduces to a Kubo response for the winding flow along the spin chain, in conjunction with the parasitic vorticity flow transverse to it. One-dimensional topological hydrodynamics can be recovered when the vorticity flow is asymptotically small. Starting with a microscopic spin-chain formulation, we focus on the asymptotic behavior of the winding transport based on the renormalized sine-Gordon equation, incorporating phase slips as well as Gilbert damping. A generic electrical device is proposed to manifest this physics. We thus suggest winding conductivity as a tangible concept that can characterize low-energy dynamics in a broad class of quantum magnets.

Absence of Spontaneous Spin Symmetry Breaking in 1D and 2D Quantum Ferromagnetic Systems with Bilinear and Biquadratic Exchange Interactions

Some measurements have shown that the second-order exchange interaction is non-negligible in ferromagnetic compounds whose microscopic interactions are described by means of half-odd integer quantum spins. In these spin systems the ground state is either ferromagnetic or antiferromagnetic when the bilinear exchange interaction is dominant. Instead, in ferromagnetic systems characterized by bilinear and biquadratic exchange interactions of comparable magnitude, the energy minimum occurs when spins are in a canting ground-state. To this aim, a one-dimensional (1D) quantum spin chain and a two-dimensional (2D) lattice of quantum spins subjected to periodic boundary conditions are modeled via the generalized quantum Heisenberg Hamiltonian containing, in addition to the isotropic and short-range bilinear exchange interaction of the Heisenberg type, a second-order interaction, the isotropic and short-range biquadratic exchange interaction between nearest-neighbors quantum spins. For these 1D and 2D quantum systems a generalization of the Mermin–Wagner–Hohenberg theorem (also known as Mermin–Wagner–Berezinksii or Coleman theorem) is given. It is demonstrated, by means of quantum statistical arguments, based on Bogoliubov’s inequality, that, at any finite temperature, (1) there is absence of long-range order and that (2) the law governing the vanishing of the order parameter is the same as in the bilinear case for both 1D and 2D quantum ferromagnetic systems. The physical implications of the absence of a spontaneous spin symmetry breaking in 1D spin chains and 2D spin lattices modeled via a generalized quantum Heisenberg Hamiltonian are discussed.

Perfect Integrability and Gaudin Models

We suggest the notion of perfect integrability for quantum spin chains and conjecture that quantum spin chains are perfectly integrable. We show the perfect integrability for Gaudin models associated to simple Lie algebras of all finite types, with periodic and regular quasi-periodic boundary conditions.

Entanglement properties of disordered quantum spin chains with long-range antiferromagnetic interactions

We examine the concurrence and entanglement entropy in quantum spin chains with random long-range couplings, spatially decaying with a power-law exponent $\alpha$. Using the strong disorder renormalization group (SDRG) technique, we find by analytical solution of the master equation a strong disorder fixed point, characterized by a fixed point distribution of the couplings with a finite dynamical exponent, which describes the system consistently in the regime $\alpha > 1/2$. A numerical implementation of the SDRG method yields a power law spatial decay of the average concurrence, which is also confirmed by exact numerical diagonalization. However, we find that the lowest-order SDRG approach is not sufficient to obtain the typical value of the concurrence. We therefore implement a correction scheme which allows us to obtain the leading order corrections to the random singlet state. This approach yields a power-law spatial decay of the typical value of the concurrence, which we derive both by a numerical implementation of the corrections and by analytics. Next, using numerical SDRG, the entanglement entropy (EE) is found to be logarithmically enhanced for all $\alpha$, corresponding to a critical behavior with an effective central charge $c = {\rm ln} 2$, independent of $\alpha$. This is confirmed by an analytical derivation. Using numerical exact diagonalization (ED), we confirm the logarithmic enhancement of the EE and a weak dependence on $\alpha$. For a wide range of distances $l$, the EE fits a critical behavior with a central charge close to $c=1$, which is the same as for the clean Haldane-Shastry model with a power-la-decaying interaction with $\alpha =2$. Consistent with this observation, we find using ED that the concurrence shows power law decay, albeit with smaller power exponents than obtained by SDRG.

The classical limit of mean-field quantum spin systems

The theory of strict deformation quantization of the two-sphere S2⊂R3 is used to prove the existence of the classical limit of mean-field quantum spin chains, whose ensuing Hamiltonians are denoted by HN, where N indicates the number of sites. Indeed, since the fibers A1/N=MN+1(C) and A0 = C(S2) form a continuous bundle of C*-algebras over the base space I={0}∪1/N*⊂[0,1], one can define a strict deformation quantization of A0 where quantization is specified by certain quantization maps Q1/N:Ã0→A1/N, with Ã0 being a dense Poisson subalgebra of A0. Given now a sequence of such HN, we show that under some assumptions, a sequence of eigenvectors ψN of HN has a classical limit in the sense that ω0(f) ≔ limN→∞⟨ψN, Q1/N(f)ψN⟩ exists as a state on A0 given by ω0(f)=1n∑i=1nf(Ωi), where n is some natural number. We give an application regarding spontaneous symmetry breaking, and moreover, we show that the spectrum of such a mean-field quantum spin system converges to the range of some polynomial in three real variables restricted to the sphere S2.

Insights into nature of a magnetization plateau of 3d-4f coordination polymer [Dy2Cu2]n from a spin-1/2 Ising-Heisenberg orthogonal-dimer chain

The ground state and magnetization process of an exactly solved spin-1/2 Ising-Heisenberg orthogonal-dimer chain with two different gyromagnetic factors of the Ising and Heisenberg spins are investigated in detail. It is shown that the investigated quantum spin chain exhibits up to seven possible ground states depending on a mutual interplay of the magnetic field, intra- and inter-dimer coupling constants. More specifically, the frustrated and modulated quantum antiferromagnetic phases are responsible in zero-temperature magnetization curves for a zero magnetization plateau. The intermediate 1/11- and 5/11-plateaus emerge due to the frustrated and modulated quantum ferrimagnetic phases, while the intermediate 9/11- and 10/11-plateaus can be attributed to the quantum and classical ferrimagnetic phases. It is conjectured that the magnetization plateau experimentally observed in a high-field magnetization curve of 3d-4f heterobimetallic coordination polymer [{Dy(hfac)2(CH3OH)}2{Cu(dmg)(Hdmg)}2]n (H2dmg = dimethylglyoxime; Hhfac = 1,1,1,5,5,5-hexafluoropentane-2,4-dione) could be attributed to the classical and quantum ferrimagnetic phases.

Influence of XY anisotropy on a magnetoelectric effect in spin-1/2 XY chain in a transverse magnetic field

A magnetoelectric effect according to Katsura-Nagaosa-Balatsky mechanism in spin-1/2 XY chain in transverse magnetic field is considered. A spatial orientation of the electric field is chosen to provide an exact solution of the model in terms of free spinless fermions. The simplest model of quantum spin chain demonstrating a magnetoelectric effect, a zero temperature case of the spin-1/2 XX chain in a transverse magnetic field with Katsura-Nagaosa-Balatsky mechanism, is considered. The model has the simplest possible form of the magnetization, polarization and susceptibility functions, depending on electric and magnetic fields in a most simple form. For the case of arbitrary XY anisotropy, a non-monotonous dependence of magnetization on the XY anisotropy parameter is figured out. This non-uniform behaviour is governed by the critical point which is connected with the possibility to drive the system gapless or gapped by the electric field. Singularities of the magnetoelectric susceptibility at the critical value of system parameters are shown.

Controlled quantum state transfer in XX spin chains at the Quantum Speed Limit

The Quantum Speed Limit (QSL) can be found in many different situations, in particular in the propagation of information through quantum spin chains. In homogeneous chains it implies that taking information from one extreme of the chain to the other will take a time O(N/2), where N is the chain length. Using Optimal Control Theory we design control pulses that achieve near perfect population transfer between the extremes of the chain at times on the order of N/2. Our results show that the control pulses that govern the dynamical behavior of chains with different lengths are closely related. The pulses were constructed for control schemes involving one or two actuators in chains with exchange couplings without static disorder. Our results also show that the two actuator scheme is considerably more robust against the presence of static disorder than the scheme that uses just a single one.