Spin-rotation Symmetry Research Articles

Excitation spectra of quantum matter without quasiparticles. II. Random t−J models

We present numerical solutions of the spectral functions of $t$-$J$ models with random and all-to-all exchange and global SU($M$) spin rotation symmetry. The solutions are obtained from the saddle-point equations of the large volume limit, followed by the large $M$ limit. These saddle point equations involve Green's functions for fractionalized spinons and holons carrying emergent U(1) gauge charges, obeying relations similar to those of the Sachdev-Ye-Kitaev (SYK) models. The low frequency spectral functions are compared with an analytic analysis of the operator scaling dimensions, with good agreement. We also compute the low frequency and temperature behavior of gauge-invariant observables: the electron Green's function, the local spin susceptibility and the optical conductivity; along with the temperature dependence of the d.c. resistivity. The time reparameterization soft mode (equivalent to the boundary graviton in holographically dual models of two-dimensional quantum gravity) makes important contributions to all observables, and provides a linear-in-temperature contribution to the d.c. resistivity.

Correlated fragile topology: A parton approach

A fragile topological insulator (FTI) can be viewed as an almost-atomic insulator, with emergent negative charges localized at certain real-space points, even though the underlying lattice Hilbert space contains only positively charged states. Fragile topology in free-fermion systems has been fruitfully studied using modern topological band theory. However, the concept is well defined even for strongly correlated systems, and fragile states that cannot be realized within free-fermion band theory exist abundantly. In this work we propose a rather general parton construction for such correlation-enabled FTIs. In our parton construction the associated gauge symmetries are completely Higgsed, resulting in only short-range entangled states. The effective negative charges in the FTIs emerge naturally as the remnants of negatively charged partons. For spinful electrons with $SU(2)$ spin-rotation symmetry, the fragile phases can be viewed as FTIs of charge-2, spin singlet bosonic Cooper pairs. We discuss a few examples of correlated FTIs for both spinless and spinful fermions, including some ``featureless Mott insulators'' on the honeycomb lattice previously discussed in the literature.

Magnetic soliton: From two to three components with SO(3) symmetry

Recent theoretical and experimental research has explored magnetic solitons in binary Bose-Einstein condensates (BECs). Here we demonstrate that such solitons are part of an SO(3) soliton family when embedded within a full three-component spin-1 manifold with spin-rotational symmetry. To showcase this, we have experimentally created a new type of domain wall magnetic soliton (DWMS) obtained by 90 degree rotations, which consist of a boundary between easy-axis and easy-plane polar phases. Collisions between SO(3) solitons are investigated by numerically solving the Gross-Pitaevskii equations, which exhibit novel properties including rotation and dissipation of soliton spin polarization.

Mesoscopic conductance fluctuations and noise in disordered Majorana wires

Superconducting wires with broken time-reversal and spin-rotational symmetries can exhibit two distinct topological gapped phases and host bound Majorana states at the phase boundaries. When the wire is tuned to the transition between these two phases and the gap is closed, Majorana states become delocalized leading to a peculiar critical state of the system. We study transport properties of this critical state as a function of the length $L$ of a disordered multichannel wire. Applying a non-linear supersymmetric sigma model of symmetry class D with two replicas, we identify the average conductance, its variance and the third cumulant in the whole range of $L$ from the Ohmic limit of short wires to the regime of a broad conductance distribution when $L$ exceeds the correlation length of the system. In addition, we calculate the average shot noise power and variance of the topological index for arbitrary $L$. The general approach developed in the paper can also be applied to study combined effects of disorder and topology in wires of other symmetries.

Coupling of lattice, spin, and intraconfigurational excitations of Eu3+ in Eu2ZnIrO6

In Eu2ZnIrO6, effectively two atoms are active i.e. Ir is magnetically active, which results in complex magnetic ordering within the Ir sublattice at low temperature. On the other hand, although Eu is a van-vleck paramagnet, it is active in the electronic channels involving 4f 6 crystal-field split levels. Phonons, quanta of lattice vibration, involving vibration of atoms in the unit cell, are intimately coupled with both magnetic and electronic degrees of freedom (DoF). Here, we report a comprehensive study focusing on the phonons as well as intra-configurational excitations in double-perovskite Eu2ZnIrO6. Our studies reveal strong coupling of phonons with the underlying magnetic DoF reflected in the renormalization of the phonon self-energy parameters well above the spin-solid phase (TN ~ 12 K) till temperature as high as ~ 3TN, evidences broken spin rotational symmetry deep into the paramagnetic phase. In particular, all the observed first-order phonon modes show softening of varying degree below ~3TN, and low-frequency phonons become sharper, while the high-frequency phonons show broadening attributed to the additional available magnetic damping channels. We also observed a large number of high-energy modes, 39 in total, attributed to the electronic transitions between 4f-levels of the rare-earth Eu3+ ion and these modes shows anomalous temperature evolution as well as mixing of the crystal-field split levels attributed to the strong coupling of electronic and lattice DoF.

Heisenberg-Kitaev model in a magnetic field: 1/S expansion

The exact solution of Kitaev's spin-$1/2$ honeycomb spin-liquid model has sparked an intense search for Mott insulators hosting bond-dependent Kitaev interactions, of which $\mathrm{Na}_{2}\mathrm{IrO}_{3}$ and $\alpha-\mathrm{RuCl}_{3}$ are prime examples. Subsequently, it has been proposed that also spin-$1$ and spin-$3/2$ analogs of Kitaev interactions may occur in materials with strong spin-orbit coupling. As a minimal model to describe these Kitaev materials, we study the Heisenberg-Kitaev Hamiltonian in a consistent $1/S$ expansion, with $S$ being the spin size. We present a comprehensive study of this model in the presence of an external magnetic field applied along two different directions, [001] and [111], for which an intricate classical phase diagram has been reported. In both settings, we employ spin-wave theory in a number of ordered phases to compute phase boundaries at the next-to-leading order in $1/S$ and show that quantum corrections substantially modify the classical phase diagram. More broadly, our work presents a consistent route to investigate the leading quantum corrections in spin models that break spin-rotational symmetry.

Topological theory of Lieb-Schultz-Mattis theorems in quantum spin systems

The Lieb-Schultz-Mattis (LSM) theorem states that a spin system with translation and spin rotation symmetry and half-integer spin per unit cell does not admit a gapped symmetric ground state lacking fractionalized excitations. That is, the ground state must be gapless, spontaneously break a symmetry, or be a gapped spin liquid. Thus, such systems are natural spin-liquid candidates if no ordering is found. In this work, we give a much more general criterion that determines when an LSM-type theorem holds in a spin system. For example, we consider quantum magnets with arbitrary space group symmetry and/or spin-orbit coupling. Our criterion is intimately connected to recent work on the general classification of topological phases with spatial symmetries and also allows for the computation of an "anomaly" associated with the existence of an LSM theorem. Moreover, our framework is also general enough to encompass recent works on "SPT-LSM" theorems where the system admits a gapped symmetric ground state without fractionalized excitations, but such a ground state must still be non-trivial in the sense of symmetry-protected topological (SPT) phases.

Transport in magnetically doped one-dimensional wires: can the helical protection emerge without the global helicity?

We study the phase diagram and transport properties of arbitrarily doped quantum wires functionalized by magnetic adatoms. The appropriate theoretical model for these systems is a dense one-dimensional Kondo lattice (KL) which consists of itinerant electrons interacting with localized quantum magnetic moments. We discover the novel phase of the locally helical metal where transport is protected from a destructive influence of material imperfections. Paradoxically, such a protection emerges without a need of the global helicity, which is inherent in all previously studied helical systems and requires breaking the spin-rotation symmetry. We explain the physics of this protection of the new type, find conditions, under which it emerges, and discuss possible experimental tests. Our results pave the way to the straightforward realization of the protected ballistic transport in quantum wires made of various materials.

Gapped Z2 spin liquid in the breathing kagome Heisenberg antiferromagnet

We investigate the spin-1/2 Heisenberg antiferromagnet on the kagome lattice with breathing anisotropy (i.e. with weak and strong triangular units), constructing an improved simplex Resonating Valence Bond (RVB) ansatz by successive applications (up to three times) of local quantum gates which implement a filtering operation on the bare nearest-neighbor RVB state. The resulting Projected Entangled Pair State involves a small number of variational parameters (only one at each level of application) and preserves full lattice and spin-rotation symmetries. Despite its simple analytic form, the simplex RVB provides very good variational energies at strong and even intermediate breathing anisotropy. We show that it carries $Z_2$ topological order which does not fade away under the first few applications of the quantum gates, suggesting that the RVB topological spin liquid becomes a competing ground state candidate for the kagome antiferromagnet at large breathing anisotropy.

Chiral ferromagnetism beyond Lifshitz invariants

We consider a contribution $w_{\text{ch}}$ to the micromagnetic energy density that is linear with respect to the first spatial derivatives of the local magnetization direction. For a generalized 2D Rashba ferromagnet, we present a microscopic analysis of this contribution and, in particular, demonstrate that it cannot be expressed through Lifshitz invariants beyond the linear order in the spin-orbit coupling (SOC) strength. Terms in $w_{\text{ch}}$ beyond Lifshitz invariants emerge as a result of spin rotation symmetry breaking caused by SOC. Effects of these terms on the phase diagram of magnetic states and spin-wave dispersion are discussed. Finally, we present a classification of terms in $w_{\text{ch}}$, allowed by symmetry, for each crystallographic point group.

Classical phase diagram of the Rashba-Hubbard model in the strongly correlated limit on square lattice

In this work, we investigate the interacting electrons on a square lattice in the presence of Rashba spin-orbit coupling. We first obtain the effective spin model from the Rashba-Hubbard model in the strongly correlated limit using the second perturbation theory. The effective spin model includes isotropic Heisenberg terms, nearest- and next-nearest-neighbor interactions, as well as the anisotropic ones as Kane-Mele and Dzyaloshinski-Moriya interactions. We proceed to study the influence of Rashba spin-orbit coupling on the stability of the magnetic phases of isotropic Heisenberg using Luttinger-Tisza and variational minimization classical methods. Our classical calculations show that the anisotropic terms leads to the instability of the Neel, classical degenerate and collinear phases of the isotropic Heisenberg model on the square lattice into an incommensurate planar phase. The spiral magnetic order in the two-dimensional frustrated magnets can be disordered by considering the quantum fluctuations. In a heterostructure including a noncollinear magnet and a singlet superconductor, singlet Cooper pairs can be converted to triplet pairings due to the broken spin rotational symmetry. Therefore, we can engineer a topological superconductor using noncollinear magnet in a heterostructure system.

Variety of order-by-disorder phases in the asymmetric J1−J2 zigzag ladder: From the delta chain to the J1−J2 chain

We study an asymmetric $J_1$-$J_2$ zigzag ladder consisting of two different spin-$\frac{1}{2}$ antiferromagnetic (AFM; $J_2$, $\gamma J_2>0$) Heisenberg legs coupled by zigzag-shaped ferromagnetic (FM; $J_1<0$) inter-leg interaction. On the basis of density-matrix renormalization group based calculations the ground-state phase diagram is obtained as functions of $\gamma$ and $J_2/|J_1|$. It contains four kinds of frustration-induced ordered phases except a trivial FM phase. Two of the ordered phases are valence bond solid (VBS) with spin-singlet dimerization, which is a rather conventional order by disorder. Still, it is interesting to note that the VBS states possess an Affleck-Kennedy-Lieb-Tasaki-type topological hidden order. The remaining two phases are ferrimagnetic orders, each of which is distinguished by commensurate or incommensurate spin-spin correlation. It is striking that the ferrimagnetic orders are not associated with geometrical symmetry breaking; instead, the global spin-rotation symmetry is broken. In other words, the system lowers its energy via the FM inter-leg interaction by polarizing both of the AFM Heisenberg legs. This is a rare type of order by disorder. Besides, the incommensurate ferrimagnetic state appears as a consequence of the competition between a polarization and a critical Tomonaga-Luttinger-liquid behavior in the AFM Heisenberg legs.

Rotational-permutational dual-pairing and long-lived spin order.

Quantum systems in contact with a thermal environment experience coherent and incoherent dynamics. These drive the system back toward thermal equilibrium after an initial perturbation. The relaxation process involves the reorganization of spin state populations and the decay of spin state coherences. In general, individual populations and coherences may exhibit different relaxation time constants. Particular spin configurations may exhibit exceptionally long relaxation time constants. Such spin configurations are known as long-lived spin order. The existence of long-lived spin order is a direct consequence of the symmetries of the system. For nuclear spin systems, rotational and permutational symmetries are of fundamental importance. Based on the Schur-Weyl duality theorem, we describe a theoretical framework for the study of rotational and permutational dual-symmetries in the context of long-lived spin order. Making use of the proposed formalism, we derive refined bounds on the number on long-lived spin populations and coherences for systems exhibiting rotational-permutational dual-symmetries.

Topological properties of a generalized spin–orbit-coupled Su–Schrieffer–Heeger model

We explore theoretically the effect of inter and intra cell spin-orbit couplings on topological properties of a generalized Su-Schrieffer-Heeger model with multipartite lattice structure containing even number of sites per unit cell. We show that the spin-orbit couplings enrich topological phase diagrams so that nontrivial topological regions in the space of parameters extend significantly which is suitable for potential applications. We present an analytical formula for winding number in terms of sublattice number signaling that there are two nontrivial topological phases in the space of parameters hosting twofold/fourfold degenerate zero-mode boundary states. We also find that by increasing the number of sublattices within unit cell, the nontrivial regions of topological phase diagram including twofold degenerate zero-mode edge states extend dramatically. Our symmetry investigation shows that U(1) spin rotational symmetry around the lattice direction is the crucial ingredient for the appearance of fourfold degenerate zero-mode boundary states.

Goldstone modes in the emergent gauge fields of a frustrated magnet

We consider magnon excitations in the spin-glass phase of geometrically frustrated antiferromagnets with weak exchange disorder, focussing on the nearest-neighbour pyrochlore-lattice Heisenberg model at large spin. The low-energy degrees of freedom in this system are represented by three copies of a U(1) emergent gauge field, related by global spin-rotation symmetry. We show that the Goldstone modes associated with spin-glass order are excitations of these gauge fields, and that the standard theory of Goldstone modes in Heisenberg spin glasses (due to Halperin and Saslow) must be modified in this setting.

Detection of spin-orbit torque with spin rotation symmetry

It has been recently demonstrated that spin–orbit coupling in ferromagnetic metals can generate spin current with symmetries different from the conventional spin Hall effect in nonmagnetic metals. The generated spin current can induce a spin–orbit torque on a neighboring magnetic layer with spin rotation symmetry. In this paper, we introduce a set of tools to measure this effect in a perpendicularly magnetized film, by using the second-order planar Hall effect method and spin-torque ferromagnetic resonance spectroscopy. These results are comparable to those detected by the polar magneto-optic Kerr effect technique.

Strain-Induced Spin-Nematic State and Nematic Susceptibility Arising from 2×2 Fe Clusters in KFe_{0.8}Ag_{1.2}Te_{2}.

Spin nematics break spin-rotational symmetry while maintaining time-reversal symmetry, analogous to liquid crystal nematics that break spatial rotational symmetry while maintaining translational symmetry. Although several candidate spin nematics have been proposed, the identification and characterization of such a state remain challenging because the spin-nematic order parameter does not couple directly to experimental probes. KFe_{0.8}Ag_{1.2}Te_{2} (K_{5}Fe_{4}Ag_{6}Te_{10}, KFAT) is a local-moment magnet consisting of well-separated 2×2 Fe clusters, and in its ground state the clusters order magnetically, breaking both spin-rotational and time-reversal symmetries. Using uniform magnetic susceptibility and neutron scattering measurements, we find a small strain induces sizable spin anisotropy in the paramagnetic state of KFAT, manifestly breaking spin-rotational symmetry while retaining time-reversal symmetry, resulting in a strain-induced spin-nematic state in which the 2×2 clusters act as the spin analog of molecules in a liquid crystal nematic. The strain-induced spin anisotropy in KFAT allows us to probe its nematic susceptibility, revealing a divergentlike increase upon cooling, indicating the ordered ground state is driven by a spin-orbital entangled nematic order parameter.

Quantum MonteCarlo Simulation of the Chiral Heisenberg Gross-Neveu-Yukawa Phase Transition with a Single Dirac Cone.

We present quantum MonteCarlo simulations for the chiral Heisenberg Gross-Neveu-Yukawa quantum phase transition of relativistic fermions with N=4 Dirac spinor components subject to a repulsive, local four fermion interaction in (2+1)D. Here we employ a two-dimensional lattice Hamiltonian with a single, spin-degenerate Dirac cone, which exactly reproduces a linear energy-momentum relation for all finite size lattice momenta in the absence of interactions. This allows us to significantly reduce finite size corrections compared to the widely studied honeycomb and π-flux lattices. A Hubbard term dynamically generates a mass beyond a critical coupling of U_{c}=6.76(1) as the system acquires antiferromagnetic order and SU(2) spin rotational symmetry is spontaneously broken. At the quantum phase transition, we extract a self-consistent set of critical exponents ν=0.98(1), η_{ϕ}=0.53(1), η_{ψ}=0.18(1), and β=0.75(1). We provide evidence for the continuous degradation of the quasiparticle weight of the fermionic excitations as the critical point is approached from the semimetallic phase. Finally, we study the effective "speed of light" of the low-energy relativistic description, which depends on the interaction U, but is expected to be regular across the quantum phase transition. We illustrate that the strongly coupled bosonic and fermionic excitations share a common velocity at the critical point.

Proximity effect in superconducting heterostructures with strong spin-orbit coupling and spin splitting

It has been shown that singlet Cooper pairs can be converted into triplet ones and diffuse into a ferromagnet over a long distance in a phenomenon known as the long-range proximity effect (LRPE). This happens in materials with inhomogeneous magnetism or spin-orbit coupling (SOC). Most of the previous studies focus on the cases with small SOC and exchange field. However, the physics was not clear when SOC and exchange field strength are both much greater than the disorder strength. In this work, we consider a two-dimensional system with a large Rashba-type SOC and exchange field in the case where only one band is partially occupied. We develop a generalized quasiclassical theory by projecting the Green function onto the partially occupied band (POB). We find that when the SOC energy scale is comparable with the exchange field, there is no LRPE. The reason is that the nonmagnetic impurities together with the large SOC and exchange field can effectively generate spin-flip scattering, which suppresses the proximity effect. We also show that when increasing either SOC or exchange field, the decay length of superconducting correlations can be significantly increased due to an approximately restored time reversal symmetry or spin rotation symmetry around the $z$ (out-of-plane) axis.

Correlated paramagnetism and interplay of magnetic and phononic degrees of freedom in 3d-5d coupled La2CuIrO6

Conventional paramagnetism–a state with finite magnetic moment per ion sans long range magnetic ordering, but with lowering temperature the moment each ion picks up a particular direction, breaking spin rotational symmetry, and results into long-range magnetic ordering. However, in systems with competing multiple degrees of freedom this conventional notion may easily break and results into short range correlation much above the global magnetic transition temperature. La2CuIrO6 with complex interplay of spins (s = 1/2) on Cu site and pseudo-spin (j = 1/2) on Ir site owing to strong spin–orbit coupling provides fertile ground to observe such correlated phenomena. By a comprehensive temperature dependent Raman study, we have shown the presence of such a correlated paramagnetic state in La2CuIrO6 much above the long-range magnetic ordering temperature (TN). Our observation of strong interactions of phonons, associated with Cu/Ir octahedra, with underlying magnetic degrees of freedom mirrored in the observed Fano asymmetry, which remarkably persists as high as ~3.5TN clearly signals the existence of correlated paramagnetism hence broken spin rotational symmetry. Our detailed analysis also reveals anomalous changes in the self-energy parameters of the phonon modes, i.e. mode frequencies and linewidth, below TN, providing a useful gauge for monitoring the strong coupling between phonons and magnetic degrees of freedom.