Single Plaquette Research Articles

Quantum curvature fluctuations and the cosmological constant in a single plaquette quantum gravity model

Abstract Understanding the microscopic behavior of spacetime, in particular quantum uncertainty in the Ricci scalar, is critical for developing a theory of quantum gravity and perhaps solving the cosmological constant problem. To test this, we compute this quantity for a simple but exact discrete quantum gravity model based on a single plaquette of spacetime. Our results confirm initial speculations of Wheeler from 1955 in finding a UV divergence in the quantum uncertainty. We further show that this behavior is stable under renormalization, but potentially unstable with the introduction of a cosmological constant, suggesting that a bare cosmological constant is ruled out.

Engineering the Kitaev Spin Liquid in a Quantum Dot System.

The Kitaev model on a honeycomb lattice may provide a robust topological quantum memory platform, but finding a material that realizes the unique spin-liquid phase remains a considerable challenge. We demonstrate that an effective Kitaev Hamiltonian can arise from a half-filled Fermi-Hubbard Hamiltonian where each site can experience a magnetic field in a different direction. As such, we provide a method for realizing the Kitaev spin liquid on a single hexagonal plaquette made up of 12 quantum dots. Despite the small system size, there are clear signatures of the Kitaev spin-liquid ground state, and there is a range of parameters where these signatures are predicted, allowing a potential platform where Kitaev spin-liquid physics can be explored experimentally in quantum dot plaquettes.

Localization Dynamics at the Exceptional Point of Non-Hermitian Creutz Ladder

We propose a quasi-one-dimensional non-Hermitian Creutz ladder with an entirely flat spectrum by introducing alternating gain and loss components while maintaining inversion symmetry. Destructive interference generates a flat spectrum at the exceptional point, where the Creutz ladder maintains coalesced and degenerate eigenvalues with compact localized states distributed in a single plaquette. All excitations are completely confined within the localization area, unaffected by gain and loss. Single-site excitations exhibit nonunitary dynamics with intensities increasing due to level coalescence, while multiple-site excitations may display oscillating or constant intensities at the exceptional point. These results provide insights into the fascinating dynamics of non-Hermitian localization, where level coalescence and degeneracy coexist at the exceptional point.

Flat-band localization and interaction-induced delocalization of photons

Lattices with dispersionless, or flat, energy bands have attracted substantial interest in part due to the strong dependence of particle dynamics on interactions. Using superconducting circuits, we experimentally study the dynamics of one and two particles in a single plaquette of a lattice whose band structure consists entirely of flat bands. We first observe strictly localized dynamics of a single particle, the hallmark of all-bands-flat physics. Upon initializing two particles on the same site, we see an interaction-enabled delocalized walk across the plaquette. We further find localization in Fock space for two particles initialized on opposite sides of the plaquette. These results mark the first experimental observation of a quantum walk that becomes delocalized due to interactions and establishes a key building block in superconducting circuits for studying flat-band dynamics with strong interactions.

Multiple flatbands and localized states in photonic super-Kagome lattices.

We demonstrate multiple flatbands and compact localized states (CLSs) in a photonic super-Kagome lattice (SKL) that exhibits coexistence of singular and nonsingular flatbands within its unique band structure. Specifically, we find that the upper two flatbands of an SKL are singular-characterized by singularities due to band touching with their neighboring dispersive bands at the Brillouin zone center. Conversely, the lower three degenerate flatbands are nonsingular and remain spectrally isolated from other dispersive bands. The existence of such two distinct types of flatbands is experimentally demonstrated by observing stable evolution of the CLSs with various geometrical shapes in a laser-written SKL. We also discuss the classification of the flatbands in momentum space, using band-touching singularities of the Bloch wave functions. Furthermore, we validate this classification in real space based on unit cell occupancy of the CLSs in a single SKL plaquette. These results may provide insights for the study of flatband transport, dynamics, and nontrivial topological phenomena in other relevant systems.

Basic elements for simulations of standard-model physics with quantum annealers: Multigrid and clock states

We explore the potential of D-Wave's quantum annealers for computing some of the basic components required for quantum simulations of Standard Model physics. By implementing a basic multigrid (including "zooming") and specializing Feynman-clock algorithms, D-Wave's Advantage is used to study harmonic and anharmonic oscillators relevant for lattice scalar field theories and effective field theories, the time evolution of a single plaquette of SU(3) Yang-Mills lattice gauge field theory, and the dynamics of flavor entanglement in four neutrino systems.

Berry phases of vison transport in Z2 topologically ordered states from exact fermion-flux lattice dualities

We develop an exact map of all states and operators from 2D lattices of spins-$1/2$ into lattices of fermions and bosons with mutual semionic statistical interaction that goes beyond previous dualities of $\mathbb{Z}_2$ lattice gauge theories because it does not rely on imposing local conservation laws and captures the motion of ``charges'' and ``fluxes'' on equal footing. This map allows to explicitly compute the Berry phases for the transport of fluxes in a large class of symmetry enriched topologically ordered states with emergent $\mathbb{Z}_2$ gauge fields that includes chiral, non-chiral, abelian or non-abelian, that can be perturbatively connected to models where the visons are static and the emergent fermionic spinons have a non-interacting dispersion. The numerical complexity of computing such vison phases reduces therefore to computing overlaps of ground states of free-fermion Hamiltonians. Among other results, we establish numerically the conditions under which the Majorana-carrying flux excitation in Ising-Topologically-Ordered states enriched by translations acquires $0$ or $\pi$ phase when moving around a single plaquette.

Degenerate plaquette physics as key ingredient of high-temperature superconductivity in cuprates

We study the physics of high-temperature cuprate superconductors starting from the highly degenerate four-site plaquette of the t-t^{prime} -U Hubbard model as a reference system. The degeneracy causes strong fluctuations when a lattice of plaquettes is constructed. We show that there is a large binding energy between holes when a set of four plaquettes is considered. The next-nearest-neighbour hopping t^{prime} plays a crucial role in the formation of these strongly bound electronic bipolarons whose coherence at lower temperature could be the explanation for superconductivity. A complementary approach is cluster dual fermion starting from a single degenerate plaquette, which contains the relevant short-ranged fluctuations from the beginning. It gives d-wave superconductivity as the leading instability under a reasonably broad range of parameters. The origin of the pseudogap is also discussed in terms of the coupling of degenerate plaquettes. Thus, some of the essential elements of cuprate superconductivity appear from the local plaquette physics.

Preparation of the SU(3) lattice Yang-Mills vacuum with variational quantum methods

Studying QCD and other gauge theories on quantum hardware requires the preparation of physically interesting states. The Variational Quantum Eigensolver (VQE) provides a way of performing vacuum state preparation on quantum hardware. In this work, VQE is applied to pure SU(3) lattice Yang-Mills on a single plaquette and one dimensional plaquette chains. Bayesian optimization and gradient descent were investigated for performing the classical optimization. Ansatz states for plaquette chains are constructed in a scalable manner from smaller systems using domain decomposition and a stitching procedure analogous to the Density Matrix Renormalization Group (DMRG). Small examples are performed on IBM's superconducting Manila processor.

Topological Wannier cycles induced by sub-unit-cell artificial gauge flux in a sonic crystal.

Gauge fields play a major role in understanding quantum effects. For example, gauge flux insertion into single unit cells is crucial towards detecting quantum phases and controlling quantum dynamics and classical waves. However, the potential of gauge fields in topological materials studies has not been fully exploited. Here, we experimentally demonstrate artificial gauge flux insertion into a single plaquette of a sonic crystal with a gauge phase ranging from 0 to 2π. We insert the gauge flux through a three-step process of dimensional extension, engineering a screw dislocation and dimensional reduction. Additionally, the single-plaquette gauge flux leads to cyclic spectral flows across multiple bandgaps that manifest as topological boundary states on the plaquette and emerge only when the flux-carrying plaquette encloses the Wannier centres. We termed this phenomenon as the topological Wannier cycle. This work paves the way towards sub-unit-cell gauge flux, enabling future studies on synthetic gauge fields and topological materials.

Gluon field digitization via group space decimation for quantum computers

Efficient digitization is required for quantum simulations of gauge theories. Schemes based on discrete subgroups use fewer qubits at the cost of systematic errors. We systematize this approach by deriving a single plaquette action for approximating general continuous gauge groups through integrating out field fluctuations. This provides insight into the effectiveness of these approximations, and how they could be improved. We accompany the scheme by simulations of pure gauge over the largest discrete subgroup of $SU(3)$ up to the third order.

Collapses-revivals phenomena induced by weak magnetic flux in diamond chain**Project supported the National Natural Science Foundation of China (Grant Nos. 11974053, 11674026, 11274255, 11305132, and 11475027) and China Scholarship Council (CSC).

We investigate the quantum dynamical behaviors of bosons in a diamond chain with weak magnetic flux (WMF), including Landau–Zener tunnelling, Bloch oscillations, localization phenomenon, and collapses-revivals phenomena. We observed that collapses-revivals phenomena can occur in diamond chain with WMF and cannot exist in the strong magnetic flux case as the previous study (Chang N N and Xue J K, 2018, Chin. Phys. B 27 105203). Induced by WMF, the energy band for the system varies from gapless to gapped structure. The position of the extrema of probability amplitude for ground state can also be altered by WMF within a single diamond plaquette. As a consequence, the transitions between different dynamical behaviors of bosons in diamond chain can be manipulated by WMF, depending on its initial configurations.

Emergent phase space description of unitary matrix model

We show that large N phases of a 0 dimensional generic unitary matrix model (UMM) can be described in terms of topologies of two dimensional droplets on a plane spanned by eigenvalue and number of boxes in Young diagram. Information about different phases of UMM is encoded in the geometry of droplets. These droplets are similar to phase space distributions of a unitary matrix quantum mechanics (UMQM) ((0 + 1) dimensional) on constant time slices. We find that for a given UMM, it is possible to construct an effective UMQM such that its phase space distributions match with droplets of UMM on different time slices at large N . Therefore, large N phase transitions in UMM can be understood in terms of dynamics of an effective UMQM. From the geometry of droplets it is also possible to construct Young diagrams corresponding to U(N) representations and hence different large N states of the theory in momentum space. We explicitly consider two examples: single plaquette model with TrU2 terms and Chern-Simons theory on S3. We describe phases of CS theory in terms of eigenvalue distributions of unitary matrices and find dominant Young distributions for them.

Ground states of a system of classical spins on an anisotropic triangular lattice and the spin-liquid problem in NiGa2S4 and FeGa2S4 compounds

It is shown that the ground states of a system of classical spins on an anisotropic triangular lattice with interactions within an elementary triangular plaquette can be constructed by minimizing the energy of a single plaquette. Even in the case when all three angles between plaquette spins are different, there exist five global ground-state configurations with equal energies. The most complex of these is an incommensurate four-sublattice conical spiral structure. Our results may shed some light on the experimentally observed spin-liquid-like disorder in ${\mathrm{NiGa}}_{2}{\mathrm{S}}_{4}$ and ${\mathrm{FeGa}}_{2}{\mathrm{S}}_{4}$ where a four-sublattice spin structure was observed.

Phase space distribution of Riemann zeros

We present the partition function of a most generic U(N) single plaquette model in terms of representations of a unitary group. Extremising the partition function in a large N limit, we obtain a relation between eigenvalues of unitary matrices and the number of boxes in the most dominant Young tableaux distribution. Since the eigenvalues of unitary matrices behave like coordinates of free fermions, whereas the number of boxes in a row is like conjugate momenta of the same, a relation between them allows us to provide a phase space distribution for different phases of the unitary model under consideration. This proves a universal feature that all the phases of a generic unitary matrix model can be described in terms of topology of free fermi phase space distribution. Finally, using this result and analytic properties of resolvent that satisfy the Dyson-Schwinger equation, we present a phase space distribution of unfolded zeros of the Riemann zeta function.

Bottom-up configuration-interaction emulations of ultracold fermions in entangled optical plaquettes: Building blocks of unconventional superconductivity

A microscopic configuration-interaction (CI) methodology is introduced to enable bottom-up Schroedinger-equation emulation of unconventional superconductivity in ultracold optical traps. We illustrate the method by exploring the properties of Lithium-6 atoms in a single square plaquette in the hole-pairing regime, and by analyzing the entanglement (symmetry-preserving) and disentanglement physics (via symmetry-breaking, associated with the separation of charge and spin density waves) of two coupled plaquettes in the same regime. The single-occupancy RVB states contribute only partially to the exact many-body solutions, and the CI results map onto a Hubbard Hamiltonian, but not onto the double-occupancy-excluding t-J one. For the double-plaquette case, effects brought about by breaking the symmetry between two weakly-interacting plaquettes, either by distorting, or by tilting and detuning, one of the plaquettes with respect to the other, as well as spectral changes caused by increased coupling between the two plaquettes, are explored.

Plaquette valence-bond solid in the square-latticeJ1-J2antiferromagnet Heisenberg model: A bond operator approach

We study the plaquette valence-bond solid phase of the spin-$1/2$${J}_{1}$-${J}_{2}$ antiferromagnet Heisenberg model on the square lattice within the bond-operator theory. We start by considering four $S=1/2$ spins on a single plaquette and determine the bond operator representation for the spin operators in terms of singlet, triplet, and quintet boson operators. The formalism is then applied to the ${J}_{1}$-${J}_{2}$ model and an effective interacting boson model in terms of singlets and triplets is derived. The effective model is analyzed within the harmonic approximation and the previous results of Zhitomirsky and Ueda [Phys. Rev. B 54, 9007 (1996)] are recovered. By perturbatively including cubic (triplet-triplet-triplet and singlet-triplet-triplet) and quartic interactions, we find that the plaquette valence-bond solid phase is stable within the parameter region $0.34<{J}_{2}/{J}_{1}<0.59$, which is narrower than the harmonic one. Differently from the harmonic approximation, the excitation gap vanishes at both critical couplings ${J}_{2}=0.34{J}_{1}$ and ${J}_{2}=0.59{J}_{1}$. Interestingly, for ${J}_{2}<0.48{J}_{1}$, the excitation gap corresponds to a singlet-triplet excitation at the $\ensuremath{\Gamma}$ point while, for ${J}_{2}>0.48{J}_{1}$, it is related to a singlet-singlet excitation at the $\mathbf{X}=(\ensuremath{\pi}/2,0)$ point of the tetramerized Brillouin zone.

Heavy quarkonium potential from Bethe-Salpeter wave function on the lattice

We propose a novel method for the determination of the interquark potential together with quark "kinetic mass'' $m_Q$ from the equal-time $Q\bar{Q}$ Bethe-Salpeter (BS) amplitude in lattice QCD. Our approach allows us to calculate spin-dependent $Q\bar{Q}$ potentials, e.g. the spin-spin potential, as well. In order to investigate several systematic uncertainties on such $Q\bar{Q}$ potentials, we carry out lattice QCD simulations using quenched gauge configurations generated with the single plaquette gauge action with three different lattice spacings, $a \approx$ 0.093, 0.068 and 0.047 fm, and two different physical volumes, $L \approx$ 2.2 and 3.0 fm. For heavy quarks, we employ the relativistic heavy quark (RHQ) action which can control large discretization errors introduced by large quark mass $m_Q$. The spin-independent central $Q\bar{Q}$ potential for the charmonium system yields the "Coulomb plus linear'' behavior with good scaling and small volume dependence. We explore the quark mass dependence over the wide mass range from the charm to beyond the bottom region, and then demonstrate that the spin-independent central $Q\bar{Q}$ potential in the $m_Q \to \infty$ limit is fairly consistent with the static $Q\bar{Q}$ potential obtained from Wilson loops. The spin-spin potential at finite quark mass provides a repulsive interaction with a finite range, which becomes narrower as the quark mass increases. We also discuss the applicability of the $1/m_Q$ expansion approach for the spin-spin potential.

Dynamical symmetry between spin and charge excitations studied by a plaquette mean-field approach in two dimensions

The real-time dynamics of local occupation numbers in a Hubbard model on a $6\ifmmode\times\else\texttimes\fi{}6$ square lattice is studied by means of the nonequilibrium generalization of the cluster-perturbation theory. The cluster approach is adapted to studies of two-dimensional lattice systems by using concepts of multiple-scattering theory and a component decomposition of the nonequilibrium Green's function on the Keldysh-Matsubara contour. We consider ``classical'' initial states formed as tensor products of states on $2\ifmmode\times\else\texttimes\fi{}2$ plaquettes and trace the effects of the interplaquette hopping in the final-state dynamics. Two different initially excited states are considered on an individual plaquette, a fully polarized staggered spin state (N\'eel) and a fully polarized charge-density wave (CDW). The final-state dynamics is constrained by a dynamical symmetry; i.e., the time-evolution operator and certain observables are invariant under an antiunitary transformation composed of time reversal, an asymmetric particle-hole, and a staggered sign transformation. We find an interesting interrelation between this dynamical symmetry and the separation of energy and time scales: In the case of a global excitation with all plaquettes excited, the initial N\'eel and the initial CDW states are linked by the transformation. This prevents an efficient relaxation of the CDW state on the short time scale governing the dynamics of charge degrees of freedom. Contrarily, the CDW state is found to relax much faster than the N\'eel state in the case of a local excitation on a single plaquette where the symmetry relation between the two states is broken by the coupling to the environment.

Quantum Cyclotron Orbits of a Neutral Atom Trapped in a Triple Well with a Synthetic Gauge Field

The strong effective magnetic fields with flux to the order of one flux quantum per plaquette has been realized for ultracold atoms, and the quantum cyclotron orbit of a single atom in a single plaquette exposed to the magnetic field was directly revealed recently [Phys. Rev. Lett. 107 (2011) 255301]. We study the quantum cyclotron orbits of a bosonic atom in a triple well with a synthetic gauge field, and find that the dynamics of the atom in real space is similar to a classical dynamic billiard. It is interesting that the billiard-like motion is a signature of the quantum evolution of the three-level system, and its behaviors are determined by the ratio of the two energy gaps of the three energy levels.