Session E07: Correlated Chains and Ladders

Out-of-equilibrium transverse field XY chain - non-equilibrium phase transitions, transport, and entanglement

The generalization of quantum phase transitions to non-equilibrium conditions raises a number of questions, in particular, if and how out-of-equilibrium critical phenomena can be categorized into universality classes, in analogy with thermal equilibrium.

Here we explore the non-equilibrium steady-state of an XY spin chain in a transverse magnetic field coupled at its ends to magnetic thermal reservoirs. We generalize the phase diagram to non-equilibrium conditions obtained by applying a magnetization bias to the reservoirs.

Upon increasing the bias we observe a discontinuous jump of the magnetic order parameter that coincides with a divergent the correlation length. While the first observation is a signature of a first-order transition, in equilibrium, the second arises only for continuous transitions. Thus, our findings show that out-of-equilibrium conditions allow for novel critical phenomena not possible at equilibrium. Moreover, for steady-states with a non-vanishing conductance, the entanglement entropy at the zero temperature was found to have logarithmic corrections that differ from the well-known equilibrium case.   

Estimates of the Quantum Fisher Information in the $S=1$ Anti-Ferromagnetic Heisenberg Spin Chain with Uniaxial Anisotropy

The quantum Fisher information has relevance to quantum metrology and as an entanglement measure. We focus on the $S=1$ anti-ferromagnetic Heisenberg model with uniaxial anisotropy.
Quantum Monte Carlo techniques are used to determine low temperature correlations from which the quantum Fisher
information can be estimated within the single mode approximation. The quantum Fisher information is compared to the quantum variance for the
staggered magnetization operators in the transverse direction and inequalities between the quantum Fisher information, the quantum variance and the full variance are discussed.
Both the quantum and full variance as well as the quantum Fisher information are examined at finite
temperatures above the isotropic point and at the quantum critical
point for the Haldane-N\'{e}el transition. A finite size scaling study of the quantum
Fisher information is performed at the quantum critical point and used to confirm the Ising nature of the
Haldane-N\'{e}el transition.   

Reduced density operators of finite-sized Heisenberg XXZ chains

In quantum many-body physics, reduced density operators play a central role in revealing the properties of a given system. We elaborate on this by studying finite size Heisenberg XXZ chains in the presence of periodic boundary conditions. As pointed out by F. Verstraete and J. Cirac, the admissible (2-site) local density matrices form a convex set determined by compatibility with translational invariance. The density matrices of ground states of translationally invariant nearest-neighbor Hamiltonians will define the boundary of this set. It is hard to determine this boundary without actually solving for many-body ground states, as knowledge of it would give immediate access to ground state energies of a rich class of models. Here we present studies on the size dependence of this mysterious boundary manifold. We also discuss non-analyticities of the boundary characterizing quantum phase transitions in the thermodynamic limit.   

Localization in a t − J type ladder with translational symmetry

An explicit spatial localization of a hole is shown in a two-leg t-J ladder in the presence of a staggered chemical potential, which still retains translational symmetry, by density matrix renormalization group method. Delocalization can be recovered in following cases, in which either the hidden phase string effect is turned off or a finite next-neighbor hopping t′ is added to sufficiently weaken the phase string effect. In particular, two holes are always delocalized by forming a mobile bound pair in contrast to the localized single holes, pointing to a novel pairing mechanism of strong correlation nature.   

Flexible magnetism in flexible crystals

We predict that the elastically flexible crystal, [Cu(acac)₂] [1], contains quasi-one-dimensional magnetic interactions that change dramatically when the crystal is bent. In the unbent crystal, all interchain interactions are doubly frustrated – geometrically and by the equipoise of antiferromagnetic and ferromagnetic interactions in the two planes perpendicular to the chains. We parametrize a Heisenberg model for the unbent and bent crystal from broken-symmetry density functional theory [2], revealing that the intrachain exchange interaction is an order of magnitude larger than the interchain exchange interactions. We calculate the three dimensional Néel temperature, T_N, from the chain random phase approximation (CRPA) [3], which reveals that [Cu(acac)₂] is an almost perfect Tomonaga-Luttinger liquid (TLL) with a T_N that increases by approximately 175 orders of magnitude when the material is bent. This is a proof of principle demonstration that magnetic properties can be significantly altered by bending flexible crystals.

[1] Worthy, A. et al. Nat. Chem. 2017,10, 65–69.
[2] Noodleman, L. J. Chem. Phys. 1981, 74, 5737–5743.
[3] Bocquet, M. et al. Phys. Rev. B. 2001, 64, 094425.   

Ladder-like optical conductivity in the spin-fermion model

In the nested limit of the spin-fermion model for the cuprates, 1D-type physics in the form of half-filled two-leg ladders emerges. We show that the RG flow of the corresponding ladder is towards the dMott phase, a gapped spin-liquid with short-ranged d-wave pairing correlations, and reveals an intermediate SO(5)xSO(3) symmetry. We use the results of the RG in combination with a memory-function approach to calculate the optical conductivity of the spin-fermion model in the high-frequency regime, where processes within the hotspot region dominate the transport. For finite temperature, we determine the resistivity in the zero-frequency limit. We argue that Umklapp processes play a major role. Our results show an approximate linear temperature dependence of the resistivity and a conductivity that follows a non-universal power law, qualitatively consistent with experiment.   

Spectrum of Dissipative Ising Chain

This paper extends the (0+1)D spin-boson problem to its (1+1)D version, a dissipative Ising Chain.
Monte Carlo simulation and analytic continuation methods are used to explore its phase and dynamics.
We find that, the quasi-particle excitation picture is destroyed, when the dissipation strength is greater than a critical value.   

Single-component fermion chain: emergent mode and liquids of bound states

We study the formation of bound states in a single-component Fermi chain with attractive interactions.
The phase diagram, computed from DMRG (density matrix renormalization group), shows not only a superfluid of paired fermions (pair phase) and a liquid of fermion triplets (trion phase), but also a phase (2M phase) with two gapless modes.
We argue based on our numerical data, that the single, pair, and trion phases are descendants of the 2M phase with a 2-component ("emegent") Tomonaga-Luttinger liquid theory description.   

Spontaneous SUSY breaking and NG modes in interacting Majorana chains

The relation between spontaneous symmetry breaking and Nambu-Goldstone (NG) modes has been well studied for conventional bosonic symmetries. On the other hand, the corresponding relation for spontaneous supersymmetry (SUSY) breaking in non-relativistic systems is less understood. To fill this gap, we have studied the properties of non-relativistic systems with N=2 SUSY in [1, 2]. However, properties of N=1 SUSY are still elusive.

We thus introduce and study interacting Majorana chains with N = 1 SUSY [3]. The Hamiltonian is defined by the square of a supercharge with a parameter, which is constructed solely by Majorana fermions. In the parameter space of the model, we find a particular point at which SUSY is unbroken and the ground states can be obtained analytically. We also find that SUSY is restored in the thermodynamic limit for modest values of the parameter. We prove, for large enough parameter values, that the system exhibits spontaneous SUSY breaking. We also prove the existence of NG fermions associated with this SUSY breaking, the dispersion of which is found to be cubic in momentum.

[1] N.S., H. Katsura and Y. Nakayama, Phys. Rev. D 94, 045014.
[2] N.S., H. Katsura and Y. Nakayama, Phys. Rev. D 95, 065001.
[3] N.S. and H. Katsura, arXiv:1712.01148.   

Majorana-Hubbard Ladders

Models of interacting Majorana modes may be realized in vortex lattices in superconducting films in contact with topological insulators and may be tuned to the strong interaction regime by adjusting the chemical potential. Extending the results on one- and two-dimensional Majorana-Hubbard models, here we study two- and four-leg ladders using both field theory and the {density-matrix renormalization group (DMRG)} methods, finding a phase diagram largely consistent with that proposed for the two-dimensional model on the square lattice.   

Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain-analogies to deconfined quantum critical points

We study a 1D system that shows many analogies to proposed 2D deconfined quantum critical points. Our system is a translationally invariant spin-1/2 chain with on-site Z2×Z2 symmetry and time reversal symmetry. It undergoes a direct continuous transition from a ferromagnet (FM), where one of the Z2 symmetries and the time reversal are broken, to a valence bond solid (VBS), where all on-site symmetries are restored while the translation symmetry is broken. The other Z2 symmetry remains unbroken throughout, but its presence is crucial for both the direct transition and the characterization of the VBS phase. The transition has a description in terms of either two domain wall species that "fractionalize" the VBS order parameter or in terms of partons that "fractionalize" the FM order parameter. The two descriptions are dual to each other. We also find an exact reformulation of the transition that leads to a simple field theory description that explicitly unifies the two order parameters, which can be interpreted as a new parton approach that encodes the two order parameters in instantons.   

X-ray resonant scattering study on the minor canted moment of spin-1 1 dimensional chain system NiTe2O5

A minor canted component of antiferromagnetic order below T_N ~ 30.5 K of NiTe₂O₅ was investigated by the soft x-ray resonant scattering on Ni L₃ edge. It is a S=1 (Ni²⁺) magnetic insulator composed of edge shared NiO₆ one dimensional chains along b axis with four Ni atoms per period. The nearly 90° superexchange path between two adjacent Ni stabilizes intra-chain ferromagnetic order along b axis, which is ordered antiferromagnetically between adjacent chains. A detailed analysis on the azimuthal and polarization dependence of the (010) structural forbidden peak reveals that the resonant peak is a result of interference between the anisotropic tensor susceptibility and the magnetic resonant scattering amplitude from 'up-down-down-up' minor canted moment in ac plane. The non-collinear spin structure is related to the distortion of Ni-O-Ni bonding to induce non-zero Dzyaloshinskii-Moriya interaction, and rather large spin-orbit coupling of Ni 3d orbital.   

Correlation between spatial and spectral inhomogeneities in the quasi one-dimensional purple bronze Li0.9Mo6O17

The marked deviation from Fermi liquid behavior for the quasi-one-dimensional (1D) purple bronze Li_0.9Mo₆O₁₇ (LMO) has been observed both by bulk transport and by surface-sensitive spectroscopic probes, and has generated much theoretical interest. Here we present spectroscopic scanning tunneling microscope (STM) images of 1D 'chains' on the surface of LMO. We find that the Coulomb suppression of tunneling around the Fermi energy is inhomogenous on the nanometer length scale, which necessitates a revision of the existing model of Luttinger-liquid-like behavior that was based on spatially-averaged spectroscopic techniques. We further report that chains of varying length exhibit resonances at varying energies, and we discuss the implications of this phenomenon for modeling the surface structure of LMO as a 1D quantum system.   

Slow Dynamics of the Fredkin Spin Chain

The dynamical behavior of many-particle systems is characterized by the lifetime of quasi-particles or excitations. Observables of any non-conserved quantity decay exponentially, but those of a conserved quantity relax to equilibrium with a power law (τ ∼ 1/Δ ∼ L^z). Such decay processes are associated with a dynamical exponent (e.g., z = 1 for the ballistic spread of quasi-particles and z = 2 for diffusion) that relates the spread of correlations in space and time. We present numerical results for the Fredkin model---a quantum spin chain with an unusual three-body interaction term---which exhibits a dynamical exponent z ≈ 3. We discuss our efforts to make a reliable, quantitative estimate of z and to explain the very slow dynamics in terms of a random walk executed by the excitation in Monte Carlo time.   

Dynamical spin conductivity in disordered quantum spin chains

Localization caused by disorder has a long history of study since the pioneering work of Anderson. Recently many-body localization (MBL) has been intensively studied in the field of both condensed-matter and statistical physics. Considering the detection of MBL in experiments, it is an important task to investigate on the behavior of physical quantities, especially dynamical ones, in interacting disordered systems. We study the dynamical spin conductivity in XXZ antiferromagnets with random magnetic field. We start from the XX models, which is equivalent to the free fermion system, and then include an Ising interaction. The ground state of easy-plane XXZ chains is gapless Luttinger liquid, and the system is localized by disorder when the Luttinger parameter satisfies K<3/2. We calculate dynamical spin conductivity numerically using the technique of Chebyshev matrix product states. We investigate this quantity in the low and high frequency region, and the behavior is power law in both regions. The power depends on the strength of Ising interaction in the high frequency region.