Quantum Spin Chains Research Articles

Estimating phase transition of perturbed Heisenberg quantum chain in mixtures of ground and first excited states

We show that the nearest neighbour entanglement in a mixture of ground and first excited states—a subjacent state—of the Heisenberg quantum spin chain can be used as an order parameter to detect the phase transition of the chain from a gapless spin fluid to a gapped dimer phase. We study the effectiveness of the order parameter for varying relative mixing probabilities between the ground and first excited states in the subjacent state for different system sizes, and extrapolate the results to the thermodynamic limit. We observe that the nearest neighbour concurrence can play a role of a good order parameter even if the system is in the ground state, but with a small finite probability of leaking into the first excited state. Moreover, we apply the order parameter of the subjacent state to investigate the response to separate introductions of anisotropy and of glassy disorder on the phase diagram of the model, and analyse the corresponding finite-size scale exponents and the emergent tricritical point in the former case. The anisotropic chain has a richer phase diagram which is also clearly visible by using the same order parameter.

Soliton confinement in a quantum circuit

Confinement of topological excitations into particle-like states - typically associated with theories of elementary particles - are known to occur in condensed matter systems, arising as domain-wall confinement in quantum spin chains. However, investigation of confinement in the condensed matter setting has rarely ventured beyond lattice spin systems. Here we analyze the confinement of sine-Gordon solitons into mesonic bound states in a perturbed quantum sine-Gordon model. The latter describes the scaling limit of a one-dimensional, quantum electronic circuit (QEC) array, constructed using experimentally-demonstrated QEC elements. The scaling limit is reached faster for the QEC array compared to spin chains, allowing investigation of the strong-coupling regime of this model. We compute the string tension of confinement of sine-Gordon solitons and the changes in the low-lying energy spectrum. These results, obtained using the density matrix renormalization group method, could be verified in a quench experiment using state-of-the-art QEC technologies.

Connection between Hilbert-space return probability and real-space autocorrelations in quantum spin chains

Connection between Hilbert-space return probability and real-space autocorrelations in quantum spin chains

Complexity of frustration: A new source of non-local non-stabilizerness

We advance the characterization of complexity in quantum many-body systems by examining WW-states embedded in a spin chain. Such states show an amount of non-stabilizerness or “magic”, measured as the Stabilizer Rényi Entropy, that grows logarithmically with the number of qubits/spins. We focus on systems whose Hamiltonian admits a classical point with extensive degeneracy. Near these points, a Clifford circuit can convert the ground state into a WW-state, while in the rest of the phase to which the classical point belongs, it is dressed with local quantum correlations. Topological frustrated quantum spin-chains host phases with the desired phenomenology, and we show that their ground state’s Stabilizer Rényi Entropy is the sum of that of the WW-states plus an extensive local contribution. Our work reveals that WW-states/frustrated ground states display a non-local degree of complexity that can be harvested as a quantum resource and has no counterpart in GHZ states/non-frustrated systems.

Exact quench dynamics from algebraic geometry.

We develop a systematic approach to compute physical observables of integrable spin chains with finite length. Our method is based on the Bethe ansatz solution of the integrable spin chain and computational algebraic geometry. The final results are analytic and no longer depend on Bethe roots. The computation is purely algebraic and does not rely on further assumptions or numerics. This method can be applied to compute a broad family of physical quantities in integrable quantum spin chains. We demonstrate the power of the method by computing two important quantities in quench dynamics-the diagonal entropy and the Loschmidt echo-and obtain analytic results.

Detecting Emergent Continuous Symmetries at Quantum Criticality.

New or enlarged symmetries can emerge at the low-energy spectrum of a Hamiltonian that does not possess the symmetries, if the symmetry breaking terms in the Hamiltonian are irrelevant under the renormalization group flow. We propose a tensor network based algorithm to numerically extract lattice operator approximation of the emergent conserved currents from the ground state of any quantum spin chains, without the necessity to have prior knowledge about its low-energy effective field theory. Our results for the spin-1/2 J-Q Heisenberg chain and a one-dimensional version of the deconfined quantum critical points demonstrate the power of our method to obtain the emergent lattice Kac-Moody generators. It can also be viewed as a way to find the local integrals of motion of an integrable model and the local parent Hamiltonian of a critical gapless ground state.

Dynamics of the geometric phase in inhomogeneous quantum spin chains

Dynamics of the geometric phase in inhomogeneous quantum spin chains

Deep learning of phase transitions for quantum spin chains from correlation aspects

Deep learning of phase transitions for quantum spin chains from correlation aspects

Ising analogs of quantum spin chains with multispin interactions

A new family of free fermionic quantum spin chains with multispin interactions was recently introduced. Here we show that it is possible to build standard quantum Ising chains---but with inhomogeneous couplings---which have the same spectra as the novel spin chains with multispin interactions. The Ising models are obtained by associating an antisymmetric tridiagonal matrix to the polynomials that characterize the quasienergies of the system via a modified Euclidean algorithm. For the simplest nontrivial case, corresponding to the Fendley model, the phase diagram of the inhomogeneous Ising model is investigated numerically. It is characterized by gapped phases separated by critical lines with order-disorder transitions depending on the parity of the total number of energy density operators in the Hamiltonian.

Groupoid and algebra of the infinite quantum spin chain

It is well known that certain features of a quantum theory cannot be described in the standard picture on a Hilbert space. In particular, this happens when we try to formally frame a quantum field theory, or a thermodynamic system with finite density. This forces us to introduce different types of algebras, more general than the ones we usually encounter in a standard course of quantum mechanics. We show how these algebras naturally arise in the Schwinger description of the quantum mechanics of an infinite spin chain. In particular, we use the machinery of Dirac-Feynman-Schwinger (DFS) states developed in recent works to introduce a dynamics based on the modular theory by Tomita-Takesaki, and consequently we apply this approach to describe the Ising model.

PathSum: A C++ and Fortran suite of fully quantum mechanical real-time path integral methods for (multi-)system + bath dynamics.

This paper reports the release of PathSum, a new software suite of state-of-the-art path integral methods for studying the dynamics of single or extended systems coupled to harmonic environments. The package includes two modules, suitable for system-bath problems and extended systems comprising many coupled system-bath units, and is offered in C++ and Fortran implementations. The system-bath module offers the recently developed small matrix path integral (SMatPI) and the well-established iterative quasi-adiabatic propagator path integral (i-QuAPI) method for iteration of the reduced density matrix of the system. In the SMatPI module, the dynamics within the entanglement interval can be computed using QuAPI, the blip sum, time evolving matrix product operators, or the quantum-classical path integral method. These methods have distinct convergence characteristics and their combination allows a user to access a variety of regimes. The extended system module provides the user with two algorithms of the modular path integral method, applicable to quantum spin chains or excitonic molecular aggregates. An overview of the methods and code structure is provided, along with guidance on method selection and representative examples.

Quantum criticality of a Z_{3}-symmetric spin chain with long-range interactions.

Based on large-scale density matrix renormalization group techniques, we investigate the critical behaviors of quantum three-state Potts chains with long-range interactions. Using fidelity susceptibility as an indicator, we obtain a complete phase diagram of the system. The results show that as the long-range interaction power α increases, the critical points f_{c}^{*} shift towards lower values. In addition, the critical threshold α_{c}(≈1.43) of the long-range interaction power is obtained for the first time by a nonperturbative numerical method. This indicates that the critical behavior of the system can be naturally divided into two distinct universality classes, namely the long-range (α<α_{c}) and short-range (α>α_{c}) universality classes, qualitatively consistent with the classical ϕ^{3} effective field theory. This work provides a useful reference for further research on phase transitions in quantum spin chains with long-range interaction.

Stochastic strong zero modes and their dynamical manifestations.

Strong zero modes (SZMs) are conserved operators localized at the edges of certain quantum spin chains, which give rise to long coherence times of edge spins. Here we define and analyze analogous operators in one-dimensional classical stochastic systems. For concreteness, we focus on chains with single occupancy and nearest-neighbor transitions, in particular particle hopping and pair creation and annihilation. For integrable choices of parameters we find the exact form of the SZM operators. Being in general nondiagonal in the classical basis, the dynamical consequences of stochastic SZMs are very different from those of their quantum counterparts. We show that the presence of a stochastic SZM is manifested through a class of exact relations between time-correlation functions, absent in the same system with periodic boundaries.

Operator fusion from wave-function overlap: Universal finite-size corrections and application to the Haagerup model

Given a critical quantum spin chain described by a conformal field theory (CFT) at long distances, it is crucial to understand the universal conformal data. One most important ingredient is the operator product expansion (OPE) coefficients, which describe how operators fuse into each other. It has been proposed in [Zou, Vidal, Phys. Rev. B 105, 125125] that the OPE coefficients can be computed from overlaps of low-energy wavefunctions of the spin chain. In this work, we establish that all conformal data including central charge, conformal dimensions, and OPE coefficients are encoded in the wavefunction overlaps, with universal finite-size corrections that depend on the operator content of the cyclic orbifold CFT. Thus this method allows us to numerically compute all the conformal data based solely on the low-energy eigenstates. The predictions are verified in the Ising and XXZ model. As an application, we study the recently proposed Haagerup model built from the Haagerup fusion category. We find that the CFT has central charge $c \approx 2.1$ and the lowest spin-$1$ operator in the twisted sector has scaling dimension $1 < \Delta_J \leq 1.4$.

Dynamically generated quadrupole polarization using Floquet adiabatic evolution

We investigate the nonequilibrium dynamics of the $S=1$ quantum spin chain subjected to a time-dependent external drive, where the driving frequency is adiabatically decreased as a function of time (``Floquet adiabatic evolution''). We show that when driving the rhombic anisotropy term (known as the ``two-axis countertwisting'' in the context of squeezed spin states) of a N\'eel antiferromagnet, we are able to induce an overall enhancement in the quadrupole polarization, while at the same time suppressing the staggered magnetization order. The system evolves into a new state with a net quadrupole moment and antiferroquadrupolar correlations. This state remains stable at long times once the driving frequency is kept constant. On the other hand, we find that we cannot achieve a quadrupole polarization for the symmetry-protected Haldane phase, which remains robust against such driving.

Duality, criticality, anomaly, and topology in quantum spin-1 chains

In quantum spin-1 chains, there is a nonlocal unitary transformation known as the Kennedy-Tasaki transformation ${U}_{\mathrm{KT}}$, which defines a duality between the Haldane phase and the ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ symmetry-breaking phase. In this paper, we find that ${U}_{\mathrm{KT}}$ also defines a duality between a topological Ising critical phase and a trivial Ising critical phase, which provides a ``hidden symmetry breaking'' interpretation of the topological criticality. Moreover, since the duality relates different phases of matter, we argue that a model with self-duality (i.e., invariant under ${U}_{\mathrm{KT}}$) is natural to be at a critical or multicritical point. We study concrete examples to demonstrate this argument. In particular, when $H$ is the Hamiltonian of the spin-1 antiferromagnetic Heisenberg chain, we prove that the self-dual model $H+{U}_{\mathrm{KT}}H{U}_{\mathrm{KT}}$ is exactly equivalent to a gapless spin-$1/2$ XY chain, which also implies an emergent quantum anomaly. On the other hand, we show that the topological and trivial Ising critical phases that are dual to each other meet at a multicritical point which is indeed self-dual.

Probability transport on the Fock space of a disordered quantum spin chain

Within the broad theme of understanding the dynamics of disordered quantum many-body systems, one of the simplest questions one can ask is: given an initial state, how does it evolve in time on the associated Fock-space graph, in terms of the distribution of probabilities thereon? A detailed quantitative description of the temporal evolution of out-of-equilibrium disordered quantum states and probability transport on the Fock space, is our central aim here. We investigate it in the context of a disordered quantum spin chain which hosts a disorder-driven many-body localisation transition. Real-time dynamics/probability transport is shown to exhibit a rich phenomenology, which is markedly different between the ergodic and many-body localised phases. The dynamics is for example found to be strongly inhomogeneous at intermediate times in both phases, but while it gives way to homogeneity at long times in the ergodic phase, the dynamics remain inhomogeneous and multifractal in nature for arbitrarily long times in the localised phase. Similarly, we show that an appropriately defined dynamical lengthscale on the Fock-space graph is directly related to the local spin-autocorrelation, and as such sheds light on the (anomalous) decay of the autocorrelation in the ergodic phase, and lack of it in the localised phase.

From Dual Unitarity to Generic Quantum Operator Spreading.

Dual-unitary circuits are paradigmatic examples of exactly solvable yet chaotic quantum many-body systems, but solvability naturally goes along with a degree of nongeneric behavior. By investigating the effect of weakly broken dual unitarity on the spreading of local operators, we study whether, and how, small deviations from dual unitarity recover fully generic many-body dynamics. We present a discrete path-integral formula for the out-of-time-order correlator and recover a butterfly velocity smaller than the light-cone velocity, v_{B}<v_{LC}, and a diffusively broadening operator front, two generic features of ergodic quantum spin chains absent in dual-unitary circuit dynamics. The butterfly velocity and diffusion constant are determined by a small set of microscopic quantities, and the operator entanglement of the gates has a crucial role.

Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability

Recent investigations have observed superdiffusion in integrable classical and quantum spin chains. An intriguing connection between these spin chains and Kardar-Parisi-Zhang (KPZ) universality class has emerged. Theoretical developments (e.g. generalized hydrodynamics) have highlighted the role of integrability as well as spin-symmetry in KPZ behaviour. However understanding their precise role on superdiffusive transport still remains a challenging task. The widely used quantum spin chain platform comes with severe numerical limitations. To circumvent this barrier, we focus on a classical integrable spin chain which was shown to have deep analogy with the quantum spin-$\frac{1}{2}$ Heisenberg chain. Remarkably, we find that KPZ behaviour prevails even when one considers integrability-breaking but spin-symmetry preserving terms, strongly indicating that spin-symmetry plays a central role even in the non-perturbative regime. On the other hand, in the non-perturbative regime, we find that energy correlations exhibit clear diffusive behaviour. We also study the classical analog of out-of-time-ordered correlator (OTOC) and Lyapunov exponents. We find significant presence of chaos for the integrability-broken cases even though KPZ behaviour remains robust. The robustness of KPZ behaviour is demonstrated for a wide class of spin-symmetry preserving integrability-breaking terms.

Integrable crosscaps in classical sigma models

We study the integrable boundaries and crosscaps of classical sigma models. We show that there exists a classical analog of the integrability condition and KT-relation of the boundary and crosscap states of quantum spin chains. We also classify the integrable crosscaps for various sigma models including examples which are relevant in the AdS/CFT correspondence at strong coupling.