Three-spin interactions in optical lattices and criticality in cluster Hamiltonians

Entangled unique coherent line in the ground-state phase diagram of the spin-1/2 XX chain model with three-spin interaction

Entangled spin coherent states are a type of quantum states that involve two or more spin systems that are correlated in a nonclassical way. These states can improve metrology and information processing, as they can surpass the standard quantum limit, which is the ultimate bound for precision measurements using coherent states. However, finding entangled coherent states in physical systems is challenging because they require precise control and manipulation of the interactions between the modes. In this work we show that entangled unique coherent states can be found in the ground state of the spin-1/2 XX chain model with three-spin interaction, which is an exactly solvable model in quantum magnetism. We use the spin squeezing parameter, the l_{1}-norm of coherence, and the entanglement entropy as tools to detect and characterize these unique coherent states. We find that these unique coherent states exist in a gapless spin liquid phase, where they form a line that separates two regions with different degrees of squeezing. We call this line the entangled unique coherent line, as it corresponds to the almost maximum entanglement between two halves of the system. We also study the critical scaling of the spin squeezing parameter and the entanglement entropy versus the system size.

Thermodynamics of hybrid quantum rotor devices

We investigate the thermodynamics of a hybrid quantum device consisting of two qubits collectively interacting with a quantum rotor and coupled dissipatively to two equilibrium reservoirs at different temperatures. By modeling the dynamics and the resulting steady state of the system using a collision model, we identify the functioning of the device as a thermal engine, a refrigerator, or an accelerator. In addition, we also look into the device's capacity to operate as a heat rectifier and optimize both the rectification coefficient and the heat flow simultaneously. Drawing an analogy to heat rectification and since we are interested in the conversion of energy into the rotor's kinetic energy, we introduce the concept of angular momentum rectification, which may be employed to control work extraction through an external load.

Embedding Semiclassical Periodic Orbits into Chaotic Many-Body Hamiltonians

Protecting coherent quantum dynamics from chaotic environment is key to realizations of fragile many-body phenomena and their applications in quantum technology. We present a general construction that embeds a desired periodic orbit into a family of nonintegrable many-body Hamiltonians, whose dynamics is otherwise chaotic. Our construction is based on time-dependent variational principle that projects quantum dynamics onto a manifold of low-entangled states, and it complements earlier approaches for embedding nonthermal eigenstates, known as quantum many-body scars, into thermalizing spectra. By designing terms that suppress "leakage" of the dynamics outside the variational manifold, we engineer families of Floquet models that host exact scarred dynamics, as we illustrate using a driven Affleck-Kennedy-Lieb-Tasaki model and a recent experimental realization of scars in a dimerized superconducting qubit chain.

N-Body Interactions between Trapped Ion Qubits via Spin-Dependent Squeezing

We describe a simple protocol for the single-step generation of N-body entangling interactions between trapped atomic ion qubits. We show that qubit state-dependent squeezing operations and displacement forces on the collective atomic motion can generate full N-body interactions. Similar to the Mølmer-Sørensen two-body Ising interaction at the core of most trapped ion quantum computers and simulators, the proposed operation is relatively insensitive to the state of motion. We show how this N-body gate operation allows for the single-step implementation of a family of N-bit gate operations such as the powerful N-Toffoli gate, which flips a single qubit if and only if all other N-1 qubits are in a particular state.

Frustration in a generalized kagomé Ising antiferromagnet: Exact results

We obtain the exact ground-state phase diagram of a generalized kagomé antiferromagnet with both pair and triplet interactions, J_{2} and J_{3}, respectively, in the presence of a magnetic field h appropriately tuned. We find that when the pair interaction J_{2}<0 dominates, the ground state is geometrically frustrated; on the other hand, the ground state is disordered but not frustrated when the triplet interaction J_{3} dominates, the boundaries between the two cases being at J_{3}=±J_{2}. The exact ground-state crossover lines between the two distinct types of disorder remain identifiable crossover curves at finite temperatures. In the frustrated domain, the ground state of the three-parameter model is identical to the ground state of the prototype one-parameter (J_{2}<0) model of geometrical frustration. Towards further understanding the frustration domain of the three-parameter model, a closed-form approximation (exact at zero temperature) determines solutions on a two-parameter subspace for induced magnetization and parallel magnetic susceptibility at finite fields h and temperatures T, the inverse susceptibility showing a Curie-Weiss behavior. We argue that the existence of an exact T=0 threshold magnetic field, below which the magnetization remains zero, indicates the existence of a gapped spectrum attributable to the presence of the triplet interaction J_{3}.

Heat Modulation on Target Thermal Bath via Coherent Auxiliary Bath

We study a scheme of thermal management where a three-qubit system assisted with a coherent auxiliary bath (CAB) is employed to implement heat management on a target thermal bath (TTB). We consider the CAB/TTB being ensemble of coherent/thermal two-level atoms (TLAs), and within the framework of collision model investigate the characteristics of steady heat current (also called target heat current (THC)) between the system and the TTB. It demonstrates that with the help of the quantum coherence of ancillae the magnitude and direction of heat current can be controlled only by adjusting the coupling strength of system-CAB. Meanwhile, we also show that the influences of quantum coherence of ancillae on the heat current strongly depend on the coupling strength of system—CAB, and the THC becomes positively/negatively correlated with the coherence magnitude of ancillae when the coupling strength below/over some critical value. Besides, the system with the CAB could serve as a multifunctional device integrating the thermal functions of heat amplifier, suppressor, switcher and refrigerator, while with thermal auxiliary bath it can only work as a thermal suppressor. Our work provides a new perspective for the design of multifunctional thermal device utilizing the resource of quantum coherence from the CAB.

Quantum Simulation of Three-Body Interactions in Weakly Driven Quantum Systems

The realization of effective Hamiltonians featuring many-body interactions beyond pairwise coupling would enable the quantum simulation of central models underpinning topological physics and quantum computation. We overcome crucial limitations of perturbative Floquet engineering and discuss the highly accurate realization of a purely three-body Hamiltonian in superconducting circuits and molecular nanomagnets.

Resilience of the topological phases to frustration

Recently it was highlighted that one-dimensional antiferromagnetic spin models with frustrated boundary conditions, i.e. periodic boundary conditions in a ring with an odd number of elements, may show very peculiar behavior. Indeed the presence of frustrated boundary conditions can destroy the local magnetic orders presented by the models when different boundary conditions are taken into account and induce novel phase transitions. Motivated by these results, we analyze the effects of the introduction of frustrated boundary conditions on several models supporting (symmetry protected) topological orders, and compare our results with the ones obtained with different boundary conditions. None of the topological order phases analyzed are altered by this change. This observation leads naturally to the conjecture that topological phases of one-dimensional systems are in general not affected by topological frustration.

Long-Range Multibody Interactions and Three-Body Antiblockade in a Trapped Rydberg Ion Chain

Trapped Rydberg ions represent a flexible platform for quantum simulation and information processing that combines a high degree of control over electronic and vibrational degrees of freedom. The possibility to individually excite ions to high-lying Rydberg levels provides a system where strong interactions between pairs of excited ions can be engineered and tuned via external laser fields. We show that the coupling between Rydberg pair interactions and collective motional modes gives rise to effective long-range and multibody interactions consisting of two, three, and four-body terms. Their shape, strength, and range can be controlled via the ion trap parameters and strongly depends on both the equilibrium configuration and vibrational modes of the ion crystal. By focusing on an experimentally feasible quasi one-dimensional setup of ^{88}Sr^{+} Rydberg ions, we demonstrate that multibody interactions are enhanced by the emergence of soft modes associated with, e.g., a structural phase transition. This has a striking impact on many-body electronic states and results-for example-in a three-body antiblockade effect that can be employed as a sensitive probe to detect structural phase transitions in Rydberg ion chains. Our study unveils the possibilities offered by trapped Rydberg ions for studying exotic phases of matter and quantum dynamics driven by enhanced multibody interactions.

Confined Phases of One-Dimensional Spinless Fermions Coupled to Z_{2} Gauge Theory

We investigate a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical Z_{2} gauge field. The gauge field mediates long-range attraction between fermions resulting in their confinement into bosonic dimers. At strong coupling we develop an exactly solvable effective theory of such dimers with emergent constraints. Even at generic coupling and fermion density, the model can be rewritten as a local spin chain. Using the density matrix renormalization group the system is shown to form a Luttinger liquid, indicating the emergence of fractionalized excitations despite the confinement of lattice fermions. In a finite chain we observe the doubling of the period of Friedel oscillations which paves the way towards experimental detection of confinement in this system. We discuss the possibility of a Mott phase at the commensurate filling 2/3.

Engineering NonBinary Rydberg Interactions via Phonons in an Optical Lattice

Coupling electronic and vibrational degrees of freedom of Rydberg atoms held in optical tweezer arrays offers a flexible mechanism for creating and controlling atom-atom interactions. We find that the state-dependent coupling between Rydberg atoms and local oscillator modes gives rise to two- and three-body interactions which are controllable through the strength of the local confinement. This approach even permits the cancellation of two-body terms such that three-body interactions become dominant. We analyze the structure of these interactions on two-dimensional bipartite lattice geometries and explore the impact of three-body interactions on system ground state on a square lattice. Focusing specifically on a system of ^{87}Rb atoms, we show that the effects of the multibody interactions can be maximized via a tailored dressed potential within a trapping frequency range of the order of a few hundred kilohertz and for temperatures corresponding to a >90% occupation of the atomic vibrational ground state. These parameters, as well as the multibody induced timescales, are compatible with state-of-the-art arrays of optical tweezers. Our work shows a highly versatile handle for engineering multibody interactions of quantum many-body systems in most recent manifestations on Rydberg lattice quantum simulators.

Topological phase diagram of the disordered 2XY model in presence of generalized Dzyaloshinskii-Moriya interaction

The topological index of a system determines its edge physics. However, in situations such as strong disorder where due to level repulsion the spectral gap closes, the topological indices are not well-defined. In this paper, we show that the localization length of zero modes determined by the transfer matrix method reveals much more information than the topological index. The localization length can provide not only information about the topological index of the Hamiltonian itself, but it can also provide information about the topological indices of the 'relative' Hamiltonians. As a case study, we study a generalized XY model (2XY model) further augmented by a generalized Dziyaloshinskii-Moriya-like (DM) interaction parameterized by [Formula: see text] that after fermionization breaks the time-reversal invariance. The parent Hamiltonian at [Formula: see text] which belongs to the BDI class is indexed by an integer winding number while the [Formula: see text] daughter Hamiltonian which belongs to class D is specified by a Z ₂ index [Formula: see text]. We show that the localization length, in addition to determining Z ₂, can count the number of Majorana zero modes leftover at the boundary of the daughter Hamiltonian-which are not protected by the winding number anymore. Therefore the localization length outperforms the standard topological indices in two respects: (i) it is much faster and more accurate to calculate and (ii) it can count the winding number of the parent Hamiltonian by looking into the edges of the daughter Hamiltonian.

Multifunctional quantum thermal device utilizing three qubits

Quantum thermal devices which can manage heat as their electronic analogs for the electronic currents have attracted increasing attention. Here a three-terminal quantum thermal device is designed by three coupling qubits interacting with three heat baths with different temperatures. Based on the steady-state behavior solved from the dynamics of this system, it is demonstrated that such a device integrates multiple interesting thermodynamic functions. It can serve as a heat current transistor to use the weak heat current at one terminal to effectively amplify the currents through the other two terminals, to continuously modulate them ranging in a large amplitude, and even to switch on or off the heat currents. It is also found that the three currents are not sensitive to the fluctuation of the temperature at the low-temperature terminal, so it can behave as a thermal stabilizer. In addition, we can utilize one terminal temperature to ideally turn off the heat current at any one terminal and to allow the heat currents through the other two terminals, so it can be used as a thermal valve. Finally, we illustrate that this thermal device can control the heat currents to flow unidirectionally, so it has the function of a thermal rectifier.

Refrigeration beyond weak internal coupling

We investigate the performance of a three-spin quantum absorption refrigerator using a refined open quantum system model valid across all interspin coupling strengths. It describes the transition between previous approximate models for the weak and the ultrastrong coupling limit, and it predicts optimal refrigeration for moderately strong coupling, where both approximations are inaccurate. Two effects impede a more effective cooling: the coupling between the spins no longer reduces to a simple resonant energy exchange (the rotating wave approximation fails), and the interactions with the thermal baths become sensitive to the level splitting, thus opening additional heat channels between the reservoirs. We identify the modified conditions of refrigeration as a function of the interspin coupling strength, and we show that, contrary to intuition, a high-temperature work reservoir thwarts refrigeration in the strong coupling regime.

Scaling of geometric phase versus band structure in cluster-Ising models

We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by an Ising exchange interaction and external magnetic field. The various phases are studied through winding numbers. They may be ordinary phases with local order parameters or exotic ones, known as symmetry protected topologically ordered phases. Quantum phase transitions with dynamical critical exponents z=1 or z=2 are found. In particular, the criticality is analyzed through finite-size scaling of the geometric phase accumulated when the spins of the lattice perform an adiabatic precession. With this study, we quantify the scaling behavior of the geometric phase in relation to the topology and low-energy properties of the band structure of the system.

Topological Quantum Liquids with Long-Range Couplings

Very few topological systems with long-range couplings have been considered so far due to our lack of analytic approaches. Here we extend the Kitaev chain, a 1D quantum liquid, to infinite-range couplings and study its topological properties. We demonstrate that, even though topological phases are intimately linked to the notion of locality, the infinite-range couplings give rise to topological zero and nonzero energy Majorana end modes depending on the boundary conditions of the system. We show that the analytically derived properties are to a large degree stable against modifications to decaying long-range couplings. Our work opens new frontiers for topological states of matter that are relevant to current experiments, where systems with interactions of variable range can be designed.

Energy dynamics in a generalized compass chain

We investigate the energy dynamics in a generalized compass chain under an external magnetic field. We show that the energy current operators act on three contiguous sites in the absence of the magnetic field, and they are incorporated with inhomogenous Dzyaloshinskii-Moriya interactions in the presence of the magnetic field. Under these complex interactions the Hamiltonian remains an exactly solvable spin model. We study the effects of the three-site interactions and the Dzyaloshinskii-Moriya interactions on the energy spectra and phase diagram. The results have revealed that the energy current of the pristine quantum compass model is conserved due to the associated intermediate symmetries, and for other general cases such a characteristic does not exist.

Characterizing Ground and Thermal States of Few-Body Hamiltonians

The question whether a given quantum state is a ground or thermal state of a few-body Hamiltonian can be used to characterize the complexity of the state and is important for possible experimental implementations. We provide methods to characterize the states generated by two- and, more generally, k-body Hamiltonians as well as the convex hull of these sets. This leads to new insights into the question of which states are uniquely determined by their marginals and to a generalization of the concept of entanglement. Finally, certification methods for quantum simulation can be derived.

Realizing All so(N)_{1} Quantum Criticalities in Symmetry Protected Cluster Models

We show that all so(N)_{1} universality class quantum criticalities emerge when one-dimensional generalized cluster models are perturbed with Ising or Zeeman terms. Each critical point is described by a low-energy theory of N linearly dispersing fermions, whose spectrum we show to precisely match the prediction by so(N)_{1} conformal field theory. Furthermore, by an explicit construction we show that all the cluster models are dual to nonlocally coupled transverse field Ising chains, with the universality of the so(N)_{1} criticality manifesting itself as N of these chains becoming critical. This duality also reveals that the symmetry protection of cluster models arises from the underlying Ising symmetries and it enables the identification of local representations for the primary fields of the so(N)_{1} conformal field theories. For the simplest and experimentally most realistic case that corresponds to the original one-dimensional cluster model with local three-spin interactions, our results show that the su(2)_{2}≃so(3)_{1} Wess-Zumino-Witten model can emerge in a local, translationally invariant, and Jordan-Wigner solvable spin-1/2 model.

Quantum phase transitions in a chain with two- and four-spin interactions in a transverse field

We use entanglement entropy and finite-size scaling methods to investigate the ground-state properties of a spin-1/2 Ising chain with two-spin (J(2)) and four-spin (J(4)) interactions in a transverse magnetic field (B). We concentrate our study on the unexplored critical region B=1 and obtain the phase diagram of the model in the (J(4)-J(2)) plane. The phases found include ferromagnetic (F), antiferromagnetic (AF), as well as more complex phases involving spin configurations with multiple periodicity. The system presents both first- and second-order transitions separated by tricritical points. We find an unusual phase boundary on the semi-infinite segment (J(4)<-1,J(2)=0) separating the F and AF phases.

Critical behavior of a quantum chain with four-spin interactions in the presence of longitudinal and transverse magnetic fields

We study the ground-state properties of a spin-1/2 model on a chain containing four-spin Ising-like interactions in the presence of both transverse and longitudinal magnetic fields. We use entanglement entropy and finite-size scaling methods to obtain the phase diagrams of the model. Our numerical calculations reveal a rich variety of phases and the existence of multicritical points in the system. We identify phases with both ferromagnetic and antiferromagnetic orderings. We also find periodically modulated orderings formed by a cluster of like spins followed by another cluster of opposite like spins. The quantum phases in the model are found to be separated by either first- or second-order transition lines.

Critical excitation spectrum of a quantum chain with a local three-spin coupling

Using the phenomenological renormalization group (PRG), we evaluate the low-energy excitation spectrum along the critical line of a quantum spin chain having a local interaction between three Ising spins and longitudinal and transverse magnetic fields, i.e., a Turban model. The low-energy excitation spectrum found with the PRG agrees with the spectrum predicted for the (D(4),A(4)) conformal minimal model under a nontrivial correspondence between translations at the critical line and discrete lattice translations. Under this correspondence, the measurements confirm a prediction that the critical line of this quantum spin chain and the critical point of the two-dimensional three-state Potts model are in the same universality class.

Quantum simulation of a system with competing two- and three-body interactions

Quantum phase transitions occur at zero temperature, when the ground state of a Hamiltonian undergoes a qualitative change as a function of a control parameter. We consider a particularly interesting system with competing one-, two-, and three-body interactions. Depending on the relative strength of these interactions, the ground state of the system can be a product state, or it can exhibit genuine tripartite entanglement. We experimentally simulate such a system in a NMR quantum simulator and observe the different ground states. By adiabatically changing the strength of one coupling constant, we push the system from one ground state to a qualitatively different ground state. We show that these ground states can be distinguished and the transitions between them observed by measuring correlations between the spins or the expectation values of suitable entanglement witnesses.

Identifying phases of quantum many-body systems that are universal for quantum computation

Quantum computation can proceed solely through single-qubit measurements on an appropriate quantum state, such as the ground state of an interacting many-body system. We investigate a simple spin-lattice system based on the cluster-state model, and by using nonlocal correlation functions that quantify the fidelity of quantum gates performed between distant qubits, we demonstrate that it possesses a quantum (zero-temperature) phase transition between a disordered phase and an ordered "cluster phase" in which it is possible to perform a universal set of quantum gates.

Solids and supersolids of three-body interacting polar molecules on an optical lattice

We study the physics of cold polar molecules loaded into an optical lattice in the regime of strong three-body interactions, as put forward recently by Büchler et al. [Nature Phys. 3, 726 (2007)]. To this end, quantum Monte Carlo simulations, exact diagonalization, and a semiclassical approach are used to explore hard-core bosons on the 2D square lattice which interact solely by long-ranged three-body terms. The resulting phase diagram shows a sequence of solid and supersolid phases. Our findings are directly relevant for future experimental implementations and open a new route towards the discovery of a lattice supersolid phase in experiment.

Geometric phases and criticality in spin systems

A general formalism of the relation between geometric phases produced by circularly evolving interacting spin systems and their criticality behaviour is presented. This opens up the way for the use of geometric phases as a tool to probe regions of criticality without having to undergo a quantum phase transition. As a concrete example, a spin-1/2 chain with XY interactions is considered and the corresponding geometric phases are analysed. Finally, a generalization of these results to the case of an arbitrary spin system is presented.

General entanglement scaling laws from time evolution

We establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy of a distinguished block saturates, and hence follows an entanglement-boundary law. These results apply to any ground state of a gapped model resulting from dynamics generated by a local Hamiltonian, as well as, dually, to states that are generated via a sudden quench of an interaction as recently studied in the case of dynamics of quantum phase transitions. We achieve these results by exploiting ideas from quantum information theory and tools provided by Lieb-Robinson bounds. We also show that there exist noncritical fermionic systems and equivalent spin chains with rapidly decaying interactions violating this entanglement-boundary law. Implications for the classical simulatability are outlined.

Quantum phase transitions in matrix product systems

We investigate quantum phase transitions (QPTs) in spin chain systems characterized by local Hamiltonians with matrix product ground states. We show how to theoretically engineer such QPT points between states with predetermined properties. While some of the characteristics of these transitions are familiar, like the appearance of singularities in the thermodynamic limit, diverging correlation length, and vanishing energy gap, others differ from the standard paradigm: In particular, the ground state energy remains analytic, and the entanglement entropy of a half-chain stays finite. Examples demonstrate that these kinds of transitions can occur at the triple point of "conventional" QPTs.

Geometric phases and criticality in spin-chain systems

A relation between geometric phases and criticality of spin chains is established. As a result, we show how geometric phases can be exploited as a tool to detect regions of criticality without having to undergo a quantum phase transition. We analytically evaluate the geometric phase that corresponds to the ground and excited states of the anisotropic XY model in the presence of a transverse magnetic field when the direction of the anisotropy is adiabatically rotated. It is demonstrated that the resulting phase is resilient against the main sources of errors. A physical realization with ultracold atoms in optical lattices is presented.

Entanglement in spin chains and lattices with long-range Ising-type interactions

We consider N initially disentangled spins, embedded in a ring or d-dimensional lattice of arbitrary geometry, which interact via some long-range Ising-type interaction. We investigate relations between entanglement properties of the resulting states and the distance dependence of the interaction in the limit N-->infinity. We provide a sufficient condition when bipartite entanglement between blocks of L neighboring spins and the remaining system saturates and determine S(L) analytically for special configurations. We find an unbounded increase of S(L) as well as diverging correlation and entanglement length under certain circumstances. For arbitrarily large N, we can efficiently calculate all quantities associated with reduced density operators of up to ten particles.

Entanglement in a valence-bond solid state

We study entanglement in a valence-bond solid state, which describes the ground state of an Affleck-Kennedy-Lieb-Tasaki quantum spin chain, consisting of bulk spin-1's and two spin-1/2's at the ends. We characterize entanglement between various subsystems of the ground state by mostly calculating the entropy of one of the subsystems; when appropriate, we evaluate concurrences as well. We show that the reduced density matrix of a continuous block of bulk spins is independent of the size of the chain and the location of the block relative to the ends. Moreover, we show that the entanglement of the block with the rest of the sites approaches a constant value exponentially fast, as the size of the block increases. We also calculate the entanglement of (i) any two bulk spins with the rest, and (ii) the end spin-1/2's (together and separately) with the rest of the ground state.

Locality in quantum and Markov dynamics on lattices and networks

We consider gapped systems governed by either quantum or Markov dynamics, with the low-lying states below the gap being approximately degenerate. For a broad class of dynamics, we prove that ground or stationary state correlation functions can be written as a piece decaying exponentially in space plus a term set by matrix elements between the low-lying states. The key to the proof is a local approximation to the negative energy, or annihilation, part of an operator in a gapped system. Applications to numerical simulation of quantum systems and to networks are discussed.