Session H19: Spin Chains: Theory

Quantum phase transitions and stable edge magnetism in effective spin models for graphene zigzag nanoribbons

We derive and examine effective quantum spin models that allow to analyse the interaction-induced magnetic correlations among the edge states of graphene nanoribbons beyond previous mean-field theory approaches, fully accounting for quantum fluctuations. We find that the extended nature of the intra-edge couplings in the effective spin model for zigzag nanoribbons leads to a quantum phase transition at a large, finite value of the inter-edge coupling. This quantum critical point separates a quantum disordered region from a gapless phase of stable edge magnetism at weak intra-edge coupling, which includes the ground states of spin-ladder models for sufficiently wide zigzag nanoribbons. We find that narrow zigzag ribbons of only a few zigzag lines instead reside within the quantum disordered regime. To study the quantum critical behavior, the effective spin model can be related to a model of two antiferromagnetically coupled Haldane-Shastry spin-half chains with long-ranged ferromagnetic intra-chain couplings. The results for the critical exponents compare well to recent renormalization group calculations for related long-ranged interacting quantum systems.   

Two-Terminal Transport of Quantum Spin Superfluidity

We theoretically study the spin current between two quantum spin chains with easy plane anisotropy separated by an intermediate quantum spin chain with easy axis anisotropy in the same plane. Upon increasing the magnetic field, the middle section undergoes a quantum phase transition from a doubly degenerate ordered phase to a nondenerate quantum paramagnet. In the nongenerate phase, we find that zero energy magnons are exponentially suppressed by the middle section and perfectly reflected when the middle section is sufficiently long. In the degenerate phase, the tunneling is exponentially suppressed until a resonant length is reached in which there is a peak in the transmission of magnons which facilitates transfer of a spin superfluid. We identify a twist in the magnetic order connecting the two degenerate ground states in the middle region as the mechanism responsible for the enhanced tunneling at this resonant length beyond which incident magnons are perfectly reflected with opposite spin.   

Spinon deconfinement on domain walls

A valence-bond solid phase of a square-lattice antiferromagnet supports four dimer patterns (vacua) related by the Z4 lattice rotational symmetries. Such a system allows for stable domain walls between regions in different vacua. We here discuss a system in a wide-strip geometry, where boundary conditions enforce two parallel domain walls along the long direction. In this system a spin-1 excitation deconfines into two spin-1/2 spinons, even though such excitations are confined into conventional spin-1 "triplons" in the bulk because of the confining strings formed when spinons are separated. In the geometry we consider, the domain walls absorb the confining strings, leading to a finite energy of creating the spinons. We confirm this scenario by quantum Monte Carlo simulations of the J-Q spin model, showing that, by tuning the width of the strip (thedistance between the domain walls), we can control the mass of such deconfined spinon excitation.   

Non-trivial phases at intermediate rung coupling in SU(N) Heisenberg ladders

Ladder models represent a first step away from purely 1D chains into the 2D realm. Here we analyze the Hubbard ladder of N symmetric flavors in the Mott regime with one particle / site, equivalent to the SU(N) Heisenberg ladder with the defining representation at each site. We analyze the latter for N<6 using the density matrix renormalization group (DMRG) in the regime of antiferromagnetic leg and rung coupling which is also most natural for quantum simulatons in ultracold atoms. While the asymmptotic regimes of strong or weak rung coupling J_⊥ are mostly understood, the full phase diagram for arbitrary J_⊥>0 is largely unexplored for N>2. While for even N≤6, the phase diagram turns out rather plain with a single phase for J_⊥>0, we find non-trivial intermediate phases for odd N, including incommensuration for N=3 and an extremely narrow phase for N=5 reminiscent of topological phases. By inheriting the exponential numerical complexity of multiorbital models, superior technical tools are required. By focusing on flavor-symmetric models, we fully exploit the underlying SU(N) symmetry in our DMRG simulations based on the QSpace tensor library. This allows us to keep beyond a million of states for larger N which is about two orders of magnitude beyond the current state of the art.   

The dynamic structure factor in impurity-doped spin chains

The effects of impurities in spin-1/2 Heisenberg chains are recently experiencing a renewed interest due to experimental realizations in solid state systems and ultra-cold gases. The impurities effectively cut the chains into finite segments with a discrete spectrum and characteristic correlations, which have a distinct effect on the dynamic structure factor. Using bosonization and the numerical Density Matrix Renormalization Group we provide detailed quantitative predictions for the momentum and energy resolved structure factor in doped systems. Due to the impurities, spectral weight is shifted away from the antiferromagnetic wave-vector k=π into regions which normally have no spectral weight in the thermodynamic limit. The effect can be quantitatively described in terms of scaling functions, which are derived from a recurrence relation based on bosonization. We present length-averaged and k-integrated results in terms of the doping concentration.   

Novel magnetization plateaus in the spin-1/2 antiferromagnetic Heisenberg model on a kagome-strip chain

Quantum phase transitions are one of hot topics in the study of condensed matter physics. In geometrically frustrated quantum spin systems, at zero temperature, quantum phase transitions, such as magnetization plateaus, cusps, and jumps, are frequently induced by applying magnetic field. We focus on a 1D quantum spin frustrated systems, the spin-1/2 Heisenberg model on a kagome-strip chain. We study the magnetization plateaus of this model with three antiferromagnetic exchange interactions by the density-matrix renormalization group method. In a certain range of exchange parameters, we find twelve kinds of magnetization plateaus, nine of which have magnetic structures breaking either translational and/or refection symmetry spontaneously. In a most nontrivial plateau, 3/10 plateau, we find long-period magnetic structure with a period of four unit cells [1].
[1] K. Morita, T. Sugimoto, S. Sota, and T. Tohyama, arXiv:1710.00508.   

NMR relaxation rate in quasi-one-dimensional antiferromagnets

Quasi-one-dimensional antiferromagnets are good candidates to realize a Tomonaga-Luttinger liquid (TLL), describing 1D interacting quantum systems, provided 3D coupling remains small as compared to temperature. In such systems, made of weakly coupled spin chains, interchain coupling plays an important role at low temperature as it leads to a spontaneous symmetry breaking below the critical temperature. Using time-dependent numerical simulations at finite temperature [1] we have computed and studied the NMR relaxation rate in S=1/2 antiferromagnetic XXZ spin chains to address the question of the low-temperature crossover between TLL predictions and the higher-temperature regime. To understand the effect of the three-dimensional coupling on the NMR relaxation rate (close to and at the transition), we analyze the full 3D microscopic model using quantum Monte-Carlo techniques. This allows to compute dynamical correlations in imaginary time and we will discuss recent advances to perform stochastic analytic continuation to get real frequency spectra that can be compared to analytical self-consistent approximations results [2].

[1] M. Dupont, S. Capponi, N. Laflorencie, Phys. Rev. B 94, 144409 (2016)
[2] M. Dupont, S. Capponi, N. Laflorencie, E. Orignac, in preparation   

Thermal Intra-Band Magnon Scattering in Haldane Spin-One Chains

We present results from a thorough evaluation of the dynamical spin structure factor of the Haldane chain at finite temperatures,
based on a combination of exact numerical diagonalization,
finite-temperature density-matrix renormalization group calculations and quantum Monte Carlo simulations.
Simulations performed on finite open chains exhibit a sub-gap band in the thermal spin spectral function, indicative of the
localized edge-modes in the Haldane chain's ground state. Furthermore, we observe the thermal activation of a distinct low-energy contribution to
the spin spectral function with an enhanced spectral weight at low momenta that results from intra-band magnon scattering due to the thermal population of the single-magnon mode.
These findings are discussed with respect to previous results on the spin spectral function and possible future studies on
Haldane spin chain compounds based on inelastic neutron scattering experiments.   

Emergent SU(N) symmetry in disordered SO(N) magnetic chains

We show that strongly disordered magnetic chains invariant under the SO(N) group display antiferromagnetic
phases with emergent SU(N) symmetry. At zero-temperature, the phases with SU(N) emergent symmetry
develop in two different types of ground states, formed either of randomly distributed singlets of strongly bound couples of SO(N) spins (mesonic phase), or composed of singlets made out of strongly bound integer multiples of N-tuples of
spins (baryonic phase). Both phases display low-temperature excitations behaving as quarks of SU(N).
Amongst the SO(N) symmetric spin chains, we argue that the cases with N = 2, 3, 4 and 6 represent
promising candidates to realize these phases in already well-established scenarios. Our mechanism,
nevertheless, is general, depleting all possible phases of disordered chains with SO(N) symmetry in
its defining representation. The generality of our results settles them as a building block towards a
general understanding of symmetry emergence in disordered many-body problems.   

A tunable quantum spin chain with three-body interactions

We present results for a spin chain model that interpolates between the conventional quantum Heisenberg spin chain (two-body interaction) in the limit of ferromagnetic and antiferromagnetic coupling. In this model, there is a special tuning point at which the model corresponds to the recently introduced, exactly solvable Fredkin spin chain (with its three-body interaction). We solve for the low-energy properties, numerically and semi-analytically, in order to track the properties of the system as it is tuned between the extreme limits and compare our results with the known values at the Fredkin point. We identify a zero-temperature phase diagram with multiple transitions and unexpected ordered phases.   

Disorder-induced Revival of the Bose-Einstein Condensation at High Magnetic Fields in Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$)

We theoretically investigate the high magnetic field regime of the disordered quasi-one-dimensional S=1 antiferromagnetic material Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$). This compound was believed to provide the first experimental realization of the elusive Bose-glass phase in a quantum magnet [1]. I will review our recent experimental and theoretical works [2-5] in which we discovered that this many-body localized phase is actually undermined by the resurgence of long-range order with a condensation of the underlying impurities degree of freedom, leading to a novel “order-by-disorder” mechanism.

[1] R. Yu et al. Nature 489, 379–384 (2012)
[2] A. Orlova et al. Phys. Rev. Lett. 118, 067203 (2017)
[3] M. Dupont et al. Phys. Rev. Lett. 118, 067204 (2017)
[4] M. Dupont et al. Phys. Rev. B 96, 024442 (2017)
[5] A. Orlova et al. (manuscript in preparation)   

Exposing fractional spin excitations with spin current noise in one-dimensional quantum magnets

We theoretically study the spin current and its dc noise in the bulk of a XXZ spin-1/2 antiferromagnetic chain downstream of a weak potential barrier. The system is perturbed by the potential at a single point, thermalized throughout to a finite temperature, and driven at one end by a spin Hall-facilitated injection of spin excitations. We examine the spin Fano factor, defined as the spin current noise-to-signal ratio, for evidence of the fractional nature of the spin excitation hosted by the chain, and propose non-invasive methods of generating the potential and of measuring the bulk spin current and noise.