Spin Sector Research Articles

Driven Hubbard model on a triangular lattice: Tunable Heisenberg antiferromagnet with a chiral three-spin term

We study the effects of a periodically varying electric field on the Hubbard model at half-filling on a triangular lattice. The electric field is incorporated through the phase of the nearest-neighbor hopping amplitude via the Peierls prescription. When the on-site interaction $U$ is much larger than the hopping, the effective Hamiltonian $H_{eff}$ describing the spin sector can be found using a Floquet perturbation theory. To third order in the hopping, $H_{eff}$ is found to have the form of a Heisenberg antiferromagnet with three different nearest-neighbor couplings $(J_\alpha,J_\beta,J_\gamma)$ on bonds lying along the different directions. Remarkably, when the periodic driving does not have time-reversal symmetry (TRS), $H_{eff}$ is also found to have a chiral three-spin interaction in each triangle, with the coefficient $C$ of the interaction having opposite signs on up- and down-pointing triangles. Thus periodic driving which breaks TRS can simulate the effect of a perpendicular magnetic flux which is known to generate such a chiral term in the spin sector, even though our model does not have a magnetic flux. The four parameters $(J_\alpha,J_\beta,J_\gamma,C)$ depend on the amplitude, frequency and direction of the oscillating electric field. We then study the spin model as a function of these parameters using exact diagonalization and find a rich phase diagram of the ground state with seven different phases consisting of two kinds of ordered phases (colinear and coplanar) and disordered phases. Thus periodic driving of the Hubbard model on the triangular lattice can lead to an effective spin model whose couplings can be tuned over a range of values thereby producing a variety of interesting phases.

Berezinskii-Kosterlitz-Thouless transition transport in spin-triplet superconductor

As the spin-triplet superconductivity arises from the condensation of spinful Cooper pairs, its full characterization requires not only charge ordering, but also spin ordering. For a two-dimensional (2D) easy-plane spin-triplet superconductor, this na\"{i}vely seems to suggest the possibility of two distinct Berezinskii-Kosterlitz-Thouless (BKT) phase transitions, one in the charge sector and the other in the spin sector. However, it has been recognized that there are actually three possible BKT transitions, involving the deconfinement of, respectively, the conventional vortices, the merons and the half-quantum vortices with vorticity in both the charge and the spin current. By considering equal-spin-pairing spin-triplet superconductors with bulk spin degeneracy, we show how all the transitions can be characterized by the relation between the voltage drop and the spin-polarized current bias. This study reveals that, due to the hitherto unexamined transport of half-quantum vortices, there is an upper bound on the spin supercurrent in a quasi-long range ordered spin-triplet superconductor, which provides a means for half-quantum vortex detection via transport measurements and deeper understanding of fluctuation effects in superconductor-based spintronic devices.

The Ponzano–Regge cylinder and propagator for 3d quantum gravity

We investigate the propagator of 3d quantum gravity, formulated as a discrete topological path integral. We define it as the Ponzano–Regge amplitude of the solid cylinder swept by a 2d disk evolving in time. Quantum states for a 2d disk live in the tensor products of N spins, where N is the number of holonomy insertions connecting to the disk boundary. We formulate the cylindric amplitude in terms of a transfer matrix and identify its eigen-modes in terms of spin recoupling. We show that the propagator distinguishes subspaces with different total recoupled spin. This may select the vanishing overall spin sector at late time depending on the chosen cylinder boundary data, leading to an emergent symmetry scenario in the continuum limit. We discuss applications to quantum circuits and the possibility of experimental simulations of this 3d quantum gravity propagator.

Higher spin wormholes from modular bootstrap

We investigate the connection between spacetime wormholes and ensemble averaging in the context of higher spin AdS3/CFT2. Using techniques from modular bootstrap combined with some holographic inputs, we evaluate the partition function of a Euclidean wormhole in AdS3 higher spin gravity. The fixed spin sectors of the dual CFT2 exhibit features that starkly go beyond conventional random matrix ensembles: power-law ramps in the spectral form factor and potentials with a double-well/crest underlying the level statistics.

Non-equilibrium dynamics of stripes in cuprate superconductors

We use the time-dependent Gutzwiller approximation for the single-band Hubbard model to analyze the non-equilibrium dynamics for stripe ground states. In particular, we are interested in the interplay between spin and charge dynamics which is analyzed by quenching the system either in the charge or spin sector. This allows us to investigate the coupled relaxation dynamics as a function of the supplied energy. Further insight is provided by mapping the Gutzwiller dynamics onto a time-dependent Landau approach which lacks the double occupancy contribution to the time-evolution but allows to tune the coupling between spin- and charge degrees of freedom.

Formula omitted] relation and spectrum of supersymmetric [formula omitted] model without [formula omitted] symmetry

We propose a novel characterization of the exact solution of the one-dimensional supersymmetric t−J model with generic non-diagonal boundary conditions. Instead of using Bethe roots, we parameterize the eigenvalues of transfer matrix in the spin sector with their zero-roots. By constructing the t−W relation, we obtain the explicit forms of the eigenvalues of the system and the homogeneous Bethe ansatz equations. This scheme is universal and can be applied to other quantum integrable systems with or without U(1) symmetry.

Self-induced spin-orbit torques in metallic ferromagnets

We present a phenomenological theory of spin-orbit torques in a metallic ferromagnet with spin-relaxing boundaries. The model is rooted in the coupled diffusion of charge and spin in the bulk of the ferromagnet, where we account for the anomalous Hall effects as well as the anisotropic magnetoresistance in the corresponding constitutive relations for both charge and spin sectors. The diffusion equations are supplemented with suitable boundary conditions reflecting the spin-sink capacity of the environment. In inversion-asymmetric heterostructures, the uncompensated spin accumulation exerts a dissipative torque on the order parameter, giving rise to a current-dependent linewidth in the ferromagnetic resonance with a characteristic angular dependence. We compare our model to recent spin-torque ferromagnetic resonance measurements, illustrating how rich self-induced spin-torque phenomenology can arise even in simple magnetic structures.

Eightfold quantum Hall phases in a time reversal symmetry broken tight binding model

We consider a time reversal symmetry (TRS) broken Kane-Mele model superimposed with Haldane model and chart out the phase diagram using spin Chern number to investigate the fate of quantum anomalous Hall insulator (QAHI) and quantum spin Hall insulator (QSHI) phases. Interestingly, in addition to QSHI and QAHI phase, the phase diagram unveils quantum anomalous spin Hall insulator (QASHI) phase where only one spin sector is topological. We also find multicritical points where three / four topological phase boundaries coalesce. These topological phases are protected by an effective TRS and a composite anti-unitary particle-hole symmetry leading to remarkable properties of edge modes. We find spin-selective, spin-polarized and spin-neutral edge transport in QASHI, QSHI and QAHI phases respectively. Our study indicates that the robustness of the topological phase mainly depends on the spin gap which does not necessarily vanish at the Dirac points across a topological phase transition. We believe that our proposals can be tested in near future using recent experimental advancements in solid state and cold atomic systems.

SO(5) critical point in a spin-flavor Kondo device: Bosonization and refermionization solution

We investigate a well studied system of a quantum dot coupled to a Coulomb box and leads, realizing a spin-flavor Kondo model. It exhibits a recently discovered non-Fermi liquid (NFL) behavior with emergent SO(5) symmetry. Here, through a detailed bosonization and refermionization solution, we push forward our previous work and provide a consistent and complete description of the various exotic properties and phase diagram. A unique NFL phase emerges from the presence of an uncoupled Majorana fermion from the flavor sector, whereas FL-like susceptibilities result from the gapping out of a pair of Majroana fermions from the spin and flavor sectors. Other properties, such as a $T^{3/2}$ scaling of the conductance, stability under channel or spin symmetry breaking and a re-appearance of NFL behavior upon breaking the particle-hole symmetry, are all accounted for by a renormalization group treatment of the refermionized Majorana model.

Critical behaviour of hydrodynamic series

We investigate the time-dependent perturbations of strongly coupled mathcal{N} = 4 SYM theory at finite temperature and finite chemical potential with a second order phase transition. This theory is modelled by a top-down Einstein-Maxwell-dilaton description which is a consistent truncation of the dimensional reduction of type IIB string theory on AdS5×S5. We focus on spin-1 and spin-2 sectors of perturbations and compute the linearized hydrodynamic transport coefficients up to the third order in gradient expansion. We also determine the radius of convergence of the hydrodynamic mode in spin-1 sector and the lowest non-hydrodynamic modes in spin-2 sector. Analytically, we find that all the hydrodynamic quantities have the same critical exponent near the critical point θ = frac{1}{2} . Moreover, we propose a relation between symmetry enhancement of the underlying theory and vanishing of the only third order hydrodynamic transport coefficient θ1, which appears in the shear dispersion relation of a conformal theory on a flat background.

Gapless Spin Wave Transport through a Quantum Canted Antiferromagnet

In the Landau levels of a two-dimensional electron system or when flat bands are present, e.g. in twisted van der Waals bilayers, strong electron-electron interaction gives rise to quantum Hall ferromagnetism with spontaneously broken symmetries in the spin and isospin sectors. Quantum Hall ferromagnets support a rich variety of low-energy collective excitations that are instrumental to understand the nature of the magnetic ground states and are also potentially useful as carriers of quantum information. Probing such collective excitations, especially their dispersion {\omega}(k), has been experimentally challenging due to small sample size and measurement constraints. In this work, we demonstrate an all-electrical approach that integrates a Fabry-P\'erot cavity with non-equilibrium transport to achieve the excitation, wave vector selection and detection of spin waves in graphene heterostructures. Our experiments reveal gapless, linearly dispersed spin wave excitations in the E = 0 Landau level of bilayer graphene, thus providing direct experimental evidence for a predicted canted antiferromagnetic order. We show that the gapless spin wave mode propagates with a high group velocity of several tens of km/s and maintains phase coherence over a distance of many micrometers. Its dependence on the magnetic field and temperature agree well with the hydrodynamic theory of spin waves. These results lay the foundation for the quest of spin superfluidity in this high-quality material. The resonant cavity technique we developed offers a powerful and timely method to explore the collective excitation of many spin and isospin-ordered many-body ground states in van der Waals heterostructures and open the possibility of engineering magnonic devices.

Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm

We introduce a half-filled Hamiltonian of spin-half lattice fermions that can be studied with the efficient meron-cluster algorithm in any dimension. As with the usual bipartite half-filled Hubbard models, the na\"{\i}ve $U(2)$ symmetry is enhanced to $SO(4)$. On the other hand, our model has a novel spin-charge flip ${\mathbb{Z}}_{2}^{C}$ symmetry which is an important ingredient of free massless fermions. In this work we focus on one spatial dimension and show that our model can be viewed as a lattice-regularized two-flavor chiral-mass Gross-Neveu model. Our model remains solvable in the presence of the Hubbard coupling $U$, which maps to a combination of Gross-Neveu and Thirring couplings in one dimension. Using the meron-cluster algorithm we find that the ground state of our model is a valence bond solid when $U=0$. From our field theory analysis, we argue that the valence bond solid forms inevitably because of an interesting frustration between spin and charge sectors in the renormalization group flow enforced by the ${\mathbb{Z}}_{2}^{C}$ symmetry. This state spontaneously breaks translation symmetry by one lattice unit, which can be identified with a ${\mathbb{Z}}_{2}^{\ensuremath{\chi}}$ chiral symmetry in the continuum. We show that increasing $U$ induces a quantum phase transition to a critical phase described by the $SU(2{)}_{1}$ Wess-Zumino-Witten theory. The quantum critical point between these two phases is known to exhibit a novel symmetry enhancement between spin and dimer. Here we verify the scaling relations of these correlation functions near the critical point numerically. Our study opens up the exciting possibility of numerical access to similar novel phase transitions in higher dimensions in fermionic lattice models using the meron-cluster algorithm.

How Does the Planck Scale Affect Qubits?

Gedanken experiments in quantum gravity motivate generalised uncertainty relations (GURs) implying deviations from the standard quantum statistics close to the Planck scale. These deviations have been extensively investigated for the non-spin part of the wave function, but existing models tacitly assume that spin states remain unaffected by the quantisation of the background in which the quantum matter propagates. Here, we explore a new model of nonlocal geometry in which the Planck-scale smearing of classical points generates GURs for angular momentum. These, in turn, imply an analogous generalisation of the spin uncertainty relations. The new relations correspond to a novel representation of SU(2) that acts nontrivially on both subspaces of the composite state describing matter-geometry interactions. For single particles, each spin matrix has four independent eigenvectors, corresponding to two 2-fold degenerate eigenvalues ħ±(ħ+β)/2, where β is a small correction to the effective Planck’s constant. These represent the spin states of a quantum particle immersed in a quantum background geometry and the correction by β emerges as a direct result of the interaction terms. In addition to the canonical qubits states, |0⟩=|↑⟩ and |1⟩=|↓⟩, there exist two new eigenstates in which the spin of the particle becomes entangled with the spin sector of the fluctuating spacetime. We explore ways to empirically distinguish the resulting "geometric" qubits, |0′⟩ and |1′⟩, from their canonical counterparts.

Hidden structure in the spectra of strongly correlated electrons in 1D

We identify a structure in the spectra of 1D lattice models of interacting electrons, characterised by an anomalous gapped branch of elementary excitations. Focussing on a family of Bethe ansatz solvable models, where all excitations are stable against decay, we make a four-way classification of the energy spectrum along with a model belonging to each class. We find in particular that the anomalous excitation branch may switch between the spin and charge symmetry sectors without a change in the ground state. Instead it changes its nature by becoming inaccessible to the ground state.

Dynamical properties of a driven dissipative dimerized S=12 chain

We consider the dynamical properties of a gapped quantum spin system coupled to the electric field of a laser, which drives the resonant excitation of specific phonon modes that modulate the magnetic interactions. We deduce the quantum master equations governing the time-evolution of both the lattice and spin sectors, by developing a Lindblad formalism with bath operators providing an explicit description of their respective phonon-mediated damping terms. We investigate the nonequilibrium steady states (NESS) of the spin system established by a continuous driving, delineating parameter regimes in driving frequency, damping, and spin-phonon coupling for the establishment of physically meaningful NESS and their related nontrivial properties. Focusing on the regime of generic weak spin-phonon coupling, we characterize the NESS by their frequency and wave-vector content, explore their transient and relaxation behavior, and discuss the energy flow, the system temperature, and the critical role of the type of bath adopted. Our study lays a foundation for the quantitative modeling of experiments currently being designed to control coherent many-body spin states in quantum magnetic materials.

A Short Review of One-Dimensional Wigner Crystallization

The simplest possible structural transition that an electronic system can undergo is Wigner crystallization. The aim of this short review is to discuss the main aspects of three recent experimets on the one-dimensional Wigner molecule, starting from scratch. To achieve this task, the Luttinger liquid theory of weakly and strongly interacting fermions is briefly addressed, together with the basic properties of carbon nanotubes that are required. Then, the most relevant properties of Wigner molecules are addressed, and finally the experiments are described. The main physical points that are addressed are the suppression of the energy scales related to the spin and isospin sectors of the Hamiltonian, and the peculiar structure that the electron density acquires in the Wigner molecule regime.

Mixture of scalar bosons and two-color fermions in one dimension: Superfluid-insulator transitions

Superfluid-insulator transitions in a one-dimensional mixture of two-color fermions and scalar bosons are studied within the framework of the Bose-Fermi-Hubbard model. Zero-temperature phase diagrams are constructed for repulsive intraspecies interactions and attractive or repulsive interspecies couplings. In addition to the trivial Mott insulator phases, we report the emergence of new non-trivial insulator phases that depend on the sign of the boson-fermion interaction. These non-trivial insulator phases satisfy the conditions $\rho_B\pm\rho_F=n$ and $\rho_B\pm \tfrac{1}{2}\rho_F=n$, with the plus (minus) sign for repulsive (attractive) interactions and $n$ an integer. Far from fermionic half-filling, the boson-fermion interaction drives a gapless-gapped transition in the spin sector. Our findings could be observed experimentally in state-of-the-art cold-atom setups.

Integrability and spectral form factor in Chern–Simons formulation

We study the integrability from the spectral form factor in the Chern–Simons formulation. The effective action in the higher spin sector was not derived so far. Therefore, we begin from the SL(3) Chern–Simons higher spin theory. Then the dimensional reduction in this Chern–Simons theory gives the SL(3) reparametrization invariant Schwarzian theory, which is the boundary theory of an interacting theory between the spin-2 and spin-3 fields at the infrared or massless limit. We show that the Lorentzian SL(3) Schwarzian theory is dual to the integrable model, SL(3) open Toda chain theory. Finally, we demonstrate the application of open Toda chain theory from the SL(2) case. The numerical result shows that the spectral form factor loses the dip-ramp-plateau behavior, consistent with integrability. The spectrum is not a Gaussian random matrix spectrum. We also give an exact solution of the spectral form factor for the SL(3) theory. This solution provides a similar form to the SL(2) case for [Formula: see text]. Hence the SL(3) theory should also do not have a Gaussian random matrix spectrum.

Bulk-edge correspondence and topological phases in periodically driven spin-orbit coupled materials in the low-frequency limit

We study the topological phase transitions induced in spin-orbit coupled materials with buckling like silicene, germanene, stanene, etc, by circularly polarised light, beyond the high-frequency regime, and unearth many additional topological phases. We also study the robustness of these phases in the presence of uniform disorder. These phases are characterised by the spin-resolved topological invariants, , , and , which specify the spin-resolved edge states traversing the gaps at zero quasi-energy and the Floquet zone boundaries respectively. We show that for each phase boundary, and independently for each spin sector, the gap closure in the Brillouin zone occurs at a high symmetry point.

Topology and the one-dimensional Kondo-Heisenberg model

The Kondo-Heinsberg chain is an interesting model of a strongly correlated system which has a broad superconducting state with pair-density wave (PDW) order. Some of us have recently proposed that this PDW state is a symmetry-protected topological (SPT) state, and the gapped spin sector of the model supports Majorana zero modes. In this work, we reexamine this problem using a combination of numeric and analytic methods. In extensive density matrix renormalization group calculations, we find no evidence of a topological ground state degeneracy or the previously proposed Majorana zero modes in the PDW phase of this model. This result motivated us to reexamine the original arguments for the existence of the Majorana zero modes. A careful analysis of the effective continuum field theory of the model shows that the Hilbert space of the spin sector of the theory does not contain any single Majorana fermion excitations. This analysis shows that the PDW state of the doped 1D Kondo-Heisenberg model is not an SPT with Majorana zero modes.