In condensed matter, Chiral Spin Liquids (CSL) are quantum spin analogs of electronic Fractional Quantum Hall states (in the continuum) or Fractional Chern Insulators (on the lattice). As the latter, CSL are remarkable states of matter, exhibiting topological order and chiral edge modes. Preparing CSL on quantum simulators like cold atom platforms is still an open challenge. Here we propose a simple setup on a finite cluster of spin-1/2 located at the sites of a square lattice. Using a Resonating Valence Bond (RVB) non-chiral spin liquid as initial state on which fast time-modulations of strong nearest-neighbor Heisenberg couplings are applied, following different protocols (out-of-equilibrium quench or semi-adiabatic ramping of the drive), we show the slow emergence of such a CSL phase. An effective Floquet dynamics, obtained from a high-frequency Magnus expansion of the drive Hamiltonian, provides a very accurate and simple framework fully capturing the out-of-equilibrium dynamics. An analysis of the resulting prepared states in term of Projected Entangled Pair states gives further insights on the topological nature of the chiral phase. Finally, we discuss possible applications to quantum computing.
We study the two-step Floquet dynamics of the chiral
J1-
J2-
K Heisenberg model on the
4×4 torus, alternating its non-chiral Heisenberg part
HAF and its chiral plaquette part
HK, at a parameter point where the static model hosts a quasi-degenerate, spectrally isolated chiral-spin-liquid (CSL) topological doublet. The one-period propagator is computed exactly in all symmetry sectors. Decreasing the frequency, the doublet survives the drive far beyond the frequency
ωres≃11.5J1 at which folded states first cross it in quasienergy: the time-averaged energy of the Floquet eigenstates, which orders the folded spectrum, shows that the doublet remains the isolated bottom of the spectrum down to
ω≃6J1, while stroboscopic time evolution over thousands of periods shows no heating for
ω≳ωres and only slow absorption below. The quasienergy resonances of the folded regime are invisible in the average energy, identifying them as parametrically weak avoided crossings. We argue that this mechanism, stability controlled by local energy scales rather than by the extensive many-body bandwidth, is of the type expected to survive in the thermodynamic limit, where a prethermal Floquet CSL should persist for
ω above a threshold set by local scales, with heating times exponentially long in
ω/J1, a conjecture that larger clusters can now test. Consistently, the optimal
D=3 chiral PEPS of the static problem still describes the driven doublet deep in the folded regime, with an essentially unchanged local tensor. Finally, we show that the drive is realizable on existing quantum simulators, via an explicit digital pulse sequence of XY-type two-spin gates on the four bond colours of the square lattice, with an infidelity of
1.5×10−5 per period.
At high-frequency a periodically-driven quantum spin-1/2 system can emulate a chiral spin liquid (CSL) described by an effective static local chiral Hamiltonian. In contrast, at low-frequency these settings realize "Swap" models exhibiting {\it anomalous} CSL phases, in which one-way spin transport occurs at the edge although the bulk time-evolution operator over one period is trivial. In this work we explicitly construct a family of Floquet quantum spin-1/2 models on the square lattice implementing Swap models to investigate the stability of the anomalous CSL under frequency detuning and the transition to the high-frequency regime. We used the average-energy spectrum on finite-size torus and cylinders to unfold the Floquet quasi-energy spectrum over the whole frequency range and obtain the geometrical Berry phases. This enabled us to identify three regimes upon increasing detuning: i) a finite-size regime (with no folding of the Floquet spectrum), ii) an intermediate (narrow) regime with folding and very few resonances and iii) a regime with an increased density of resonances suggesting heating. At small detuning, edge modes are revealed by spectroscopic tools and from the Streda response of the system giving access to the anomalous winding number. The analysis of all the data suggests that the anomalous CSL is not continuously connected to the high-frequency CSL. We also discuss the possible occurrence of a long-lived prethermal anomalous CSL.
We propose a scheme to implement Kitaev's honeycomb model with cold atoms, based on a periodic (Floquet) drive, in view of realizing and probing non-Abelian chiral spin liquids using quantum simulators.We derive the effective Hamiltonian to leading order in the inverse-frequency expansion, and show that the drive opens up a topological gap in the spectrum without mixing the effective Majorana and vortex degrees of freedom.We address the challenge of probing the physics of Majorana fermions, while having access only to the original composite spin degrees of freedom.Specifically, we propose to detect the properties of the chiral spin liquid phase using gap spectroscopy and edge quenches in the presence of the Floquet drive.The resulting chiral edge signal, which relates to the thermal Hall effect associated with neutral Majorana currents, is found to be robust for realistically prepared states.By combining strong interactions with Floquet engineering, our work paves the way for future studies of non-Abelian excitations and quantized thermal transport using quantum simulators.
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.
Chiral spin liquids (CSLs) are exotic phases of interacting spins in two dimensions, characterized by long-range entanglement and fractional excitations. We construct a local Hamiltonian on the triangular lattice that stabilizes the Kalmeyer-Laughlin CSL without requiring fine-tuning. Our approach employs coupled-wire constructions and introduces a lattice duality to construct a solvable chiral sliding Luttinger liquid, which is driven toward the CSL phase by generic perturbations. By combining symmetry analysis and bosonization, we make sharp predictions for the ground states on quasi-one-dimensional cylinders and tori, which exhibit a fourfold periodicity in the circumference. Extensive tensor network simulations demonstrating ground-state degeneracies, fractional quasiparticles, nonvanishing long-range order parameters, and entanglement signatures confirm the emergence of the CSL in the lattice Hamiltonian.