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arXiv:1611.07964 · Nature Communications

Dynamical time-reversal symmetry breaking and photo-induced chiral spin liquids in frustrated Mott insulators

Martin Claassen, Hong‐Chen Jiang, Brian Moritz, Thomas Devereaux

Published Oct 24, 2017• 132 citations
arXivHTMLPDF

Abstract

Abstract The search for quantum spin liquids in frustrated quantum magnets recently has enjoyed a surge of interest, with various candidate materials under intense scrutiny. However, an experimental confirmation of a gapped topological spin liquid remains an open question. Here, we show that circularly polarized light can provide a knob to drive frustrated Mott insulators into a chiral spin liquid, realizing an elusive quantum spin liquid with topological order. We find that the dynamics of a driven Kagome Mott insulator is well-captured by an effective Floquet spin model, with heating strongly suppressed, inducing a scalar spin chirality S i · (S j × S k ) term which dynamically breaks time-reversal while preserving SU(2) spin symmetry. We fingerprint the transient phase diagram and find a stable photo-induced chiral spin liquid near the equilibrium state. The results presented suggest employing dynamical symmetry breaking to engineer quantum spin liquids and access elusive phase transitions that are not readily accessible in equilibrium.

DOI
10.1038/s41467-017-00876-y

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Scalar spin chirality, a three-body spin correlation that breaks time-reversal symmetry, is revealed to couple directly to circularly polarized laser. This is shown by the Floquet formalism for the periodically driven repulsive Hubbard model with a strong-coupling expansion. A systematic derivation of the effective low-energy Hamiltonian for a spin degree of freedom reveals that the coupling constant for scalar spin chirality can become significant for a situation in which the driving frequency and the on-site interaction are comparable. This implies that the scalar chirality can be induced by circularly polarized lights, or that it can be used conversely for probing the chirality in Mott insulators as a circular dichroism.
Topological phases in frustrated quantum magnetic systems have captivated researchers for decades, with the chiral spin liquid (CSL) standing out as one of the most compelling examples. Featuring long-range entanglement, topological order, and exotic fractional excitations, the CSL has inspired extensive exploration for practical realizations. In this Letter, we demonstrate that CSLs can emerge in a kagome lattice driven by vacuum quantum fluctuations over the noninteracting vacuum within a single-mode gyrotropic cavity. The gyrotropic cavity imprints quantum fluctuations with time-reversal symmetry breaking and stabilizes a robust CSL phase without external laser excitation. Moreover, we identify experimentally accessible observables-such as average photon number and transport properties-that reveal connections between photon dynamics and the emergent chiral order. Our findings establish a novel pathway for creating, controlling, and probing topological and symmetry-breaking quantum phases in strongly correlated systems.
Recently, the frustrated XY model for spins 1/2 on the honeycomb lattice has attracted a lot of attention in relation with the possibility to realize a chiral spin liquid state. This model is relevant to the physics of some quantum magnets. Using the flexibility of ultracold atom setups, we propose an alternative way to realize this model through the Mott regime of the bosonic Kane-Mele-Hubbard model. The phase diagram of this model is derived using bosonic dynamical mean-field theory. Focusing on the Mott phase, we investigate its magnetic properties as a function of frustration. We do find an emergent chiral spin state in the intermediate frustration regime. Using exact diagonalization we study more closely the physics of the effective frustrated XY model and the properties of the chiral spin state. This gapped phase displays a chiral order, breaking time-reversal and parity symmetry, but is not topologically ordered (the Chern number is zero).
Frustrated magnetism provides a rich platform for realizing exotic quantum phases in condensed matter systems. Among these, quantum spin liquids (QSLs) are a particularly intriguing class of states that exhibit no magnetic ordering and preserve all symmetries down to zero temperature. Just as conventional magnets can be thought of as spin crystals,QSLs represent their liquid analogs. This thesis explores two broad types of QSLs in two-dimensional magnets, with a focus on their dynamic properties and the nature of transitions from conventional magnetic states into QSL phases. QSLs are topological phases that host fractionalized excitations known as spinons. In these states, mobile spinons are coupled to an emergent gauge field, forming a highly entangled phase of matter. The first part of this thesis focuses on Dirac spin liquids (DSLs), a class of QSLs where spinons exhibit a gapless Dirac dispersion. To study the dynamicsof these spin liquids beyond leading-order mean-field theory, we develop a novel large-N fermionic limit of gapless spinons. In this limit, all gauge excitations are suppressed, and the leading-order corrections instead arise from order parameter fluctuations, which may condense and drive transitions into symmetry-broken phases from the parent DSL. Incorporating random phase approximation (RPA) corrections to the spin susceptibility, we find that sharp, spin-wave–like modes are recovered in the excitation spectrum. This methodology successfully captures characteristic features of the dynamics near phase transitions and in weakly symmetry-broken phases proximate to a DSL. We apply this approach to microscopic models, including the J1-J2 XXZ model on the triangular lattice and the J1-J3 XXZ model on the honeycomb lattice. These models closely represent a wide range of frustrated materials, such as triangular and honeycomb cobaltates and triangular ytterbium compounds. Our theoretical predictions show excellent agreement with experimentally measured inelastic neutron scattering spectra from these materials. Gapless spinons can also sometimes become gapped through chiral symmetry breaking, leading to the formation of a chiral spin liquid (CSL). The CSL is an archetypal bosonic realization of a fractional quantum Hall (FQH) state at half-filling, and has been proposed as a time-reversal–breaking ground state in a variety of frustrated spin models. The second part of this thesis addresses the intriguing possibility of realizing a CSL through the "melting" of a chiral spin crystal—a conventional magnet with non-coplanar ordering. Such a transition offers a physically appealing analogue to the melting of a Wigner crystal into a fermionic FQH liquid. Focusing on the kagome lattice, where chiral interactions are knownto stabilize a CSL ground state, we study the effects of additional long-range Heisenberg interactions and demonstrate a phase transition into a non-coplanar octahedral magnetic order. To describe the universal class of transition between a CSL and a non-coplanar anti-ferromagnetic order, we then develop a novel Chern-Simons–matter field theory framework, constrained by symmetry principles and symmetry fractionalization patterns. This thesis thus provides new insights into the dynamical signatures and phase transitions of quantum spin liquids, offering a bridge between theoretical models and experimental observations in frustrated magnetic systems.
Synthetic fields applied to ultracold quantum gases can realize topological phases that transcend conventional Bose and Fermi-liquid paradigms. Raman laser beams in particular are under scrutiny as a route to create synthetic fields in neutral gases to mimic ordinary magnetic and electric fields acting on charged matter. Yet external laser beams can impose heating and losses that make cooling into many-body topological phases challenging. We propose that atomic or molecular dipoles placed in optical lattices can realize a topological phase without synthetic fields by placing them in certain frustrated lattices. We use numerical modeling on a specific example to show that the interactions between dipolar fermions placed in a kagome optical lattice spontaneously break time-reversal symmetry to lead to a topological Mott insulator, a chiral topological phase generated entirely by interactions. We estimate realistic entropy and trapping parameters to argue that this intriguing phase of matter can be probed with quantum gases using a combination of recently implemented technologies.