Quantum spin liquids and anyons, used to be subjects of condensed matter physics, now are realized in various platforms of qubits, offering unprecedented opportunities to investigate fundamental physics of many-body quantum entangled states. Qubits are inevitably exposed to environment effects such as decoherence and dissipation, which are believed to be detrimental to many-body entanglement. Here, we argue that unlike the common belief decoherence and dissipation can give rise to novel topological phenomena in quantum spin liquids. We study open quantum systems of the Kitaev spin liquid and the toric code via the Lindblad master equation approach. By using exact solutions and numerical approaches, we show the dynamical occurrence of anyon condensation by decoherence and dissipation, which results in a topological transition from the initial state spin liquid to the steady state spin liquid. The mechanism of the anyon condensation transition by the Lindblad dynamics is elucidated. We also provide an insight into the relationship between the Kitaev spin liquid and the toric code in the picture of anyon condensation. Our work suggests open quantum systems to be a new venue for topological phenomena of quantum spin liquids and anyons.
Quantum spin liquids and anyons, used to be subjects of condensed matter physics, now are realized in various platforms of qubits, offering unprecedented opportunities to investigate fundamental physics of many-body quantum entangled states. Qubits are inevitably exposed to environment effects such as decoherence and dissipation, which are believed to be detrimental to many-body entanglement. Here, we argue that unlike the common belief decoherence and dissipation can give rise to novel topological phenomena in quantum spin liquids. We study open quantum systems of the Kitaev spin liquid and the toric code via the Lindblad master equation approach. By using exact solutions and numerical approaches, we show the dynamical occurrence of anyon condensation by decoherence and dissipation, which results in a topological transition from the initial state spin liquid to the steady state spin liquid. The mechanism of the anyon condensation transition by the Lindblad dynamics is elucidated. We also provide an insight into the relationship between the Kitaev spin liquid and the toric code in the picture of anyon condensation. Our work suggests open quantum systems to be a new venue for topological phenomena of quantum spin liquids and anyons.
Transitions between quantum spin liquids (QSLs) are fundamental problems lying beyond the Landau paradigm and requiring a deep understanding of the entanglement structures of QSLs called topological orders. The novel concept of anyon condensation has been proposed as a theoretical mechanism, predicting various possible transitions between topological orders, but it has long been elusive to confirm the mechanism in quantum spin systems. Here, we introduce a concrete spin model that incarnates the mechanism of the anyon condensation transition. Our model harbors two topological QSLs in different parameter regions, a non-Abelian Kitaev spin liquid (KSL) bilayer state and a resonating valence bond (RVB) state. The bilayer-KSL-to-RVB transition indeed occurs by the mechanism of anyon condensation, which we identify by using parton theories and exact diagonalization studies. Moreover, we observe “anyon confinement” phenomena in our numerical results, akin to the quark confinement in high-energy physics. Namely, non-Abelian Ising anyons of the bilayer KSL are confined in the transition to the RVB state. Implications and extensions of this study are discussed in various aspects such as (i) anyon-condensed multilayer construction of Kitaev's 16-fold way of anyon theories, (ii) an additional vison condensation transition from the RVB to a valence bond solid in the Kitaev bilayer system, (iii) dynamical anyon condensation in a non-Hermitian Kitaev bilayer, (iv) generalizations of our model to other lattice geometries, and (v) experimental realizations. This work puts together the two fascinating QSLs that are extensively studied in modern condensed matter and quantum physics into a concrete spin model, offering a comprehensive picture that unifies the anyon physics of the Kitaev spin liquids and the resonating valence bonds. Published by the American Physical Society 2024
While many-body systems can host long-ranged entangled quantum spin liquids (QSLs), the ingredients for realizing these as ground states can be prohibitively difficult. In many circumstances, one requires (i) a constrained Hilbert space and (ii) an extensive quantum superposition. The paradigmatic example is the toric code, or Z2 spin liquid, which is a superposition of closed loop states. We show how non-equilibrium Hamiltonian dynamics can provide a streamlined route toward creating such QSLs. Rather than cooling into the ground state of a Hamiltonian, we show how a simple parameter sweep can dynamically project a family of initial product states into the constrained space, giving rise to a QSL. For the toric code, this is achieved in systems with a separation in energy scales between the e- and m-anyons, where one can sweep in a way that is adiabatic (sudden) with respect to the former (latter). Although this separation of scales does not extend to the thermodynamic limit, we analytically and numerically show that this method efficiently prepares a spin liquid in finite-sized regions, which we brand ``quantum spin lakes.'' This mechanism elucidates recent experimental and numerical observations of the dynamical state preparation of the ruby lattice spin liquid in Rydberg atom arrays. In fact, the slow dynamics of m-anyons suggest that we can capture spin lake preparation by simulating the dynamics on tree lattices, which we confirm with tensor network simulations. Finally, we use this mechanism to propose new experiments, e.g., for preparing a finite-sized U(1) spin liquid as a honeycomb Rokhsar-Kivelson dimer model using Rydberg atoms -- which is remarkable given its equilibrium counterpart is unstable in 2+1D. Our work opens up a new avenue in the study of non-equilibrium physics, as well as the exploration of exotic states of finite extent in NISQ devices.
Quantum phases with topological order, such as quantum spin liquids, have been the focus of explorations for several decades. Such phases feature a number of remarkable properties including long-range quantum entanglement. Moreover, they can be potentially exploited for the realization of robust quantum computation, as exemplified by the paradigmatic toric code model. While some indications that such phases may be present in frustrated condensed matter systems have been previously reported, so far quantum spin liquids have eluded direct experimental detection. In this talk, I will show how a programmable quantum simulator based on Rydberg atom arrays can be used to realize and probe quantum spin liquid states. In our approach, atoms are placed on the links of a kagome lattice and coherent evolution under Rydberg blockade enables the transition into frustrated quantum states with no local order. We detect the onset of a quantum spin liquid phase of the toric code type by measuring topological string operators in two complementary bases. The properties of this state are further revealed using a lattice with non-trivial topology, representing a step towards the realization of a topological qubit. Our observations open the door to the controlled experimental exploration of topological quantum matter, and could enable the investigation of new methods for topologically protected quantum information processing.
The focus of our investigations in this thesis is quantum spin systems in two dimensions. We examine phase transitions between topologically distinct phases of quantum matter using the framework of tensor network states. We study the phenomena of anyon condensation and confinement in the context of tensor network states where these two notions offer a robust probe to characterize the universal features of quantum phase transitions. We do a comprehensive study of the numerical methods enabled by the tensor network formalism for the study of quantum phase transitions. We map out the phase diagram of certain exotic phases of quantum matter (namely the D(mathbbZ4) quantum double, the toric code, and the double semion model) and identify the order and the universality classes of the phase transitions between these distinct topological phases. We analyze the phase boundaries of the toric code and the double semion model which exhibit first and second order phase transitions. We investigate the class of mathbbZ2-invariant tensor network states while taking in to account the spin rotation and lattice symmetries. The resulting tensor network states allow us to map the phase diagram of mathbbZ2 spin liquids. The behavior of the system at the phase boundaries of mathbbZ2 spin liquid is governed by the condensation of spinons and visions. We also present our preliminary findings regarding the mathbbZ4-invariant tensors with SU(2) symmetry. This approach enables us to study the spin liquid states of the toric code and the double semion model in a unified framework. We give a local tensor description for the approximate ground states of the Heisenberg antiferromagnet on the kagome lattice by using the variational manifolds of just three and five parameters in the gapped mathbbZ2 spin liquid phase. The approximation of the ground states we construct have an energy density that is remarkably close to the results from the state-of-the-art density matrix renormalization group and the exact diagonalization method. By analyzing the deconfinement of anyonic excitations, we also present our findings regarding the vicinity of the variational ground state in gapped mathbbZ2 spin liquid phase.
Quantum spin liquids have fascinated condensed matter physicists for decades because of their unusual properties such as spin fractionalization and long-range entanglement. Unlike conventional symmetry breaking, the topological order underlying quantum spin liquids is hard to detect experimentally. Even theoretical models are scarce for which the ground state is established to be a quantum spin liquid. The Kitaev honeycomb model and its generalizations to other tricoordinated lattices are chief counterexamples—they are exactly solvable, harbor a variety of quantum spin liquid phases, and are also relevant for certain transition metal compounds including the polymorphs of (Na,Li) 2 IrO 3 iridates and RuCl 3 . In this review, we give an overview of the rich physics of the Kitaev model, including two-dimensional and three-dimensional fractionalization as well as dynamic correlations and behavior at finite temperatures. We discuss the different materials and argue how the Kitaev model physics can be relevant even though most materials show magnetic ordering at low temperatures.
We study a mixed-state topological transition in the non-Abelian Kitaev spin liquid driven by a bond-dephasing channel. In the vectorized picture, bond dephasing maps onto interactions between two time-reversed fractionalized Majorana systems coupled to gapped Z2 gauge fields, enabling sign-problem-free Monte Carlo simulations. We show that increasing dephasing condenses an inter-copy fermion pair, converting Ising⊠Ising to toric-code order in the Choi state and yielding intrinsically mixed-state topological order upon unfolding. More interestingly, at a temporal interface between topological and trivial Kitaev states, a Chern-number mismatch enforces a gapless Majorana mode. Dephasing then drives a mixed-state topological transition at which the gapless mode develops emergent N=1 supersymmetry. Our Monte Carlo simulations yield ν=1.27(3) and ηb≃ηf≃0.40, consistent with the exact supersymmetric values 5/4 and 2/5. The supersymmetric partners are fractionalized and appear physically as distinct gauge-invariant spin strings, providing concrete observables for future experiments.