Ferromagnetic Domain Wall and Spiral Ground States in One-Dimensional Deformed Flat-Band Hubbard Model

We construct a set of exact ground states with a localized ferromagnetic domain wall and an extended spiral structure in a quasi-one-dimensional deformed flat-band Hubbard model. In the case of quarter filling, we show the uniqueness of the ground state with a fixed magnetization. The ground states with these structures are degenerate with the all-spin-up and all-spin-down states. This property of the degeneracy is the same as the domain wall solutions in the XXZ Heisenberg–Ising model. We derive a useful recursion relation for the normalization of the domain wall ground state. Using this recursion relation, we discuss the convergence of the ground state expectation values of arbitrary local operators in the infinite-volume limit. In the ground state of the infinite-volume system, the translational symmetry is spontaneously broken by this structure. We prove that the cluster property holds for the domain wall ground state and excited states. We also estimate bounds of the ground state expectation values of several observables, such as one- and two-point functions of spin and electron number density.     

Steady Schrödinger cat state of a driven Ising chain

For short-range interacting systems, no Schrödinger cat state can be stable when their environment is in thermal equilibrium. We show, by studying a chain of two-level systems with nearest-neighbour Ising interactions, that this is possible when the surroundings consists of two heat reservoirs at different temperatures, or of a heat reservoir and a monochromatic field. The asymptotic state of the considered system can be a pure superposition of mesoscopically distinct states, the all-spin-up and all-spin-down states, at low temperatures. The main feature of our model leading to this result is the fact that the Hamiltonian of the chain and the dominant part of its coupling to the environment obey the same symmetry.     

Droplet States in the XXZ Heisenberg Chain

We consider the ground states of the ferromagnetic XXZ chain with spin up boundary conditions. The ground state of this model, restricted to a sector with a fixed number of down spins, describes a droplet of down spins in an environment of up spins. We find the exact energy and the states that describe these droplets in the limit of an infinite number of down spins. We prove that there is a gap in the spectrum above the droplet states. As the XXZ Hamiltonian has a gap above the fully magnetized ground states as well, this means that the droplet states (for sufficiently large droplets) form an isolated band. The width of this band tends to zero in the limit of infinitely large droplets. We also prove the analogous results for finite chains with periodic boundary conditions and for the infinite chain. Received: 5 September 2000 / Accepted: 8 December 2000     

The ground-state phase diagram of the spinless 1D falicov-kimball model: Numerical studies

Extrapolation of small-cluster exact-diagonalization calculations is used to study the ground state phase diagram of the spinless one-dimensional Falicov-Kimball model at half filling. Our results show that the phase diagram has an extremely simple structure for the Coulomb interactionsU≥2. Here the ground states are the most homogeneous configurations (mhc) with the smallest periods. Valence transitions are discontinuous and only of the type insulator-insulator. In this region the finite size effects are negligible and thus the picture of valence transitions is definitive. ForU<2 the phase diagram exhibits a more complicated structure. Here we have specified a domain where the ground states are the mhc and a metallic domain where the ground states are mixtures of configurations with the empty configuration. The boundary between these two domains is the boundary of discontinuous insulator-metal transitions. Unlike the caseU≥2 the valence transitions are gradual in the weak coupling limit. This work was supported by the Slovak scientific grant agency VEGA, contract No. 4177/97.     

Bosonic Realization for Boundary States in Quantum sine-Gordon Field with Boundary

Boundary operators and boundary ground states in sine-Gordon model with a fixed boundary condition are studied using bosonization and q-deformed oscillators. We also study the boundary bound state for this case.     

The renormalization group and quantum edge states

The role of edge states in phenomena like the quantum Hall effect is well known, and the basic physics has a wide field-theoretic interest. In this paper we introduce a new model exhibiting quantum Hall-like features. We show how the choice of boundary conditions for a one-particle Schrödinger equation can give rise to states localized at the edge of the system. We consider both the example of a free particle and the more involved example of a particle in a magnetic field. In each case, edge states arise from a non-trivial scaling limit involving the boundary condition, and chirality of the boundary condition plays an essential role. Second quantization of these quantum mechanical systems leads to a multi-particle ground state carrying a persistent current at the edge. We show that the theory quantized with this vacuum displays an “anomaly” at the edge which is the mark of a quantized Hall conductivity in the presence of an external magnetic field. These models therefore possess characteristics which make them indistinguishable from the quantum Hall effect at macroscopic distances. We also offer interpretations for the physics of such boundary conditions which may have a bearing on the nature of the excitations in these models.     

On Isospectral Deformations of an Inhomogeneous String

For an anyon model in two spatial dimensions described by a modular tensor category, the topological S-matrix encodes the mutual braiding statistics, the quantum dimensions, and the fusion rules of anyons. It is nontrivial whether one can compute the S-matrix from a single ground state wave function. Here, we define a class of Hamiltonians consisting of local commuting projectors and an associated matrix that is invariant under local unitary transformations. We argue that the invariant is equivalent to the topological S-matrix. The definition does not require degeneracy of the ground state. We prove that the invariant depends on the state only, in the sense that it can be computed by any Hamiltonian in the class of which the state is a ground state. As a corollary, we prove that any local quantum circuit that connects two ground states of quantum double models (discrete gauge theories) with non-isomorphic abelian groups must have depth that is at least linear in the system’s diameter. As a tool for the proof, a manifestly Hamiltonian-independent notion of locally invisible operators is introduced. This gives a sufficient condition for a many-body state not to be generated from a product state by any small depth quantum circuit; this is a many-body entanglement witness.     

Uniqueness of the Ground State in Weak Perturbations of Non-Interacting Gapped Quantum Lattice Systems

We consider a general weak perturbation of a non-interacting quantum lattice system with a non-degenerate gapped ground state. We prove that in a finite volume the dependence of the ground state on the boundary condition exponentially decays with the distance to the boundary, which implies in particular that the infinite-volume ground state is unique. Also, equivalent forms of boundary conditions for ground states of general finite quantum systems are discussed.On leave from Institute for Information Transmission Problems, Moscow, Russia.     

A model for the physical adsorption of atomic hydrogen

The formation of the holding potential of physical adsorption is studied with a model in which a hydrogen atom interacts with a perfectly imaging substrate bounded by a sharp planar surface; the exclusion of the atomic electron from the substrate is an important boundary condition in the model. The interaction energy and the dipole and quadrupole moments of the ground state are determined with a variational calculation. The polarizability tensor of the ground state and the interaction energies in the first few excited states are also determined. A quantitative analysis is given of the transition to the dispersion-force, large-separation regime using results of perturbation theory and of the variational solution for the ground state of a hydrogen atom in the presence of a nonimaging wall. The relation of results for the image model to ideas used in the modelling of experiments is discussed; this includes a treatment of image field contributions to the depolarizing field at an ad atom.     

Determinant formula for the partition function of the six-vertex model with a non-diagonal reflecting end

With the help of the F-basis provided by the Drinfeld twist or factorizing F-matrix for the open XXZ spin chain with non-diagonal boundary terms, we obtain the determinant representation of the partition function of the six-vertex model with a non-diagonal reflecting end under domain wall boundary condition.     

Charge frustration and quantum criticality for strongly correlated fermions

We study a model of strongly correlated electrons on the square lattice which exhibits charge frustration and quantum critical behavior. The potential is tuned to make the interactions supersymmetric. We establish a rigorous mathematical result which relates quantum ground states to certain tiling configurations on the square lattice. For periodic boundary conditions this relation implies that the number of ground states grows exponentially with the linear dimensions of the system. We present substantial analytic and numerical evidence that for open boundary conditions the system has gapless edge modes.     

Are There Incongruent Ground States in 2D Edwards–Anderson Spin Glasses?

We present a detailed proof of a previously announced result [1] supporting the absence of multiple (incongruent) ground state pairs for 2D Edwards–Anderson spin glasses (with zero external field and, e.g., Gaussian couplings): if two ground state pairs (chosen from metastates with, e.g., periodic boundary conditions) on ℤ² are distinct, then the dual bonds where they differ form a single doubly-infinite, positive-density domain wall. It is an open problem to prove that such a situation cannot occur (or else to show – much less likely in our opinion – that it indeed does happen) in these models. Our proof involves an analysis of how (infinite-volume) ground states change as (finitely many) couplings vary, which leads us to a notion of zero-temperature excitation metastates, that may be of independent interest. Received: 3 December 2000/ Accepted: 30 April 2001     

Effect of grain-boundary conditions on polytype transformations in close-packed crystals

Within the framework of a modified Ising model, the effect of the boundary conditions (“free ends” and periodic boundary conditions) on the polytype structure stability is studied in close-packed crystals. Using the ground state diagrams, feasible structures and transformation induced by an external field are identified. An analysis of the model system dimensions and long- and short-range many-body interaction on the shape of the ground state diagrams under different boundary conditions is made. The temperature effects on the polytype structure characteristics are discussed in detail. It is shown that both at the absolute zero and finite temperatures, the effects of the boundary conditions on certain properties could be predominant.__________This revised version was published online in May 2005 with a correction on affiliation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 61–66, November 2004.     

Thermal entanglement versus mixture in a spin chain: Generation of maximally entangled mixed states

We study the two-body entanglement and mixture in a three-qubit XXZ spin chain in thermal equilibrium state at temperature T with an external magnetic field B. The effects of the magnetic field, the anisotropy and the temperature on the entanglement and mixture are considered. We show that the ground states in this system are fully characterized and distinguished by both entanglement and mixture. Thermal entanglement versus the mixture of all two-spin states is investigated. All pairwise states provide an upper bound on the entanglement for a fixed mixture, and some part of the boundary reaches the boundary allowed by physics. As a result, maximally entangled mixed states can be generated by controlling magnetic field and temperature. Especially, in the ground state of the whole system, the explicit forms of maximally entangled mixed states are given. The results provide a new way to generate maximally entangled mixed states and control entanglement.     

Two-dimensional Rydberg gases and the quantum hard-squares model

We study a two-dimensional lattice gas of atoms that are photoexcited to Rydberg states in which they interact via the van?der?Waals interaction. We explore the regime of dominant nearest-neighbor interaction where this system is intimately connected with a quantum version of Baxter's hard-squares model. We show that the strongly correlated ground state of the Rydberg gas can be analytically described by a projected entangled pair state that constitutes the ground state of the quantum hard-squares model. This correspondence allows us to identify a phase boundary where the Rydberg gas undergoes a transition from a disordered (liquid) phase to an ordered (solid) phase.     

Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions

An important characteristic of topological band insulators is the necessary presence of in-gap edge states on the sample boundary. We utilize this fact to show that when the boundary is reconnected with a twist, there are always zero-energy defect states. This provides a natural connection among novel defects in the two-dimensional p{x}+ip{y} superconductor, the Kitaev model, the fractional quantum Hall effect, and the one-dimensional domain wall of polyacetylene.     

A two-dimensional isotropic quantum antiferromagnet with unique disordered ground state

We continue the study of valence-bond solid antiferromagnetic quantum Hamiltonians. These Hamiltonians are invariant under rotations in spin space. We prove that a particular two-dimensional model from this class (the spin-3/2 model on the hexagonal lattice) has a unique ground state in the infinite-volume limit and hence no Néel order. Moreover, all truncated correlation functions decay exponentially in this ground state. We also characterize all the finite-volume ground states of these models (in every dimension), and prove that the two-point correlation function of the spin-2 square lattice model with periodic boundary conditions has exponential decay.     

Electronic and thermal properties of B2-type AlRE intermetallic compounds: A first principles study

The ground state electronic structure and thermal properties of B₂-type intermetallic compounds AlRE (RE: Pm, Sm, Eu, Tb, Gd and Dy) have been studied using a self-consistent tight-binding linear muffin-tin orbital (TB-LMTO) method at ambient as well as at high pressure. These compounds show metallic behavior under ambient condition. The band structure, total energy, density of states and ground state properties like lattice parameter, bulk modulus are calculated in the present work. The Debye-Grüneisen model is used to calculate the Debye temperature and the Grüneisen constant. The calculated results are in good agreement with the reported experimental and other theoretical results. The variation in the Debye temperature with pressure has also been reported. We present a detailed analysis of the role of f electrons of RE in the AlRE system.     

On Gapped Phases with a Continuous Symmetry and Boundary Operators

We discuss the role of compact symmetry groups, G, in the classification of gapped ground state phases of quantum spin systems. We consider two representations of G on infinite subsystems. First, in arbitrary dimensions, we show that the ground state spaces of models within the same G-symmetric phase carry equivalent representations of the group for each finite or infinite sublattice on which they can be defined and on which they remain gapped. This includes infinite systems with boundaries or with non-trivial topologies. Second, for two classes of one-dimensional models, by two different methods, for G=SU(2) in one, and G?SU(d), in the other we construct explicitly an ‘excess spin’ operator that implements rotations of half of the infinite chain on the GNS Hilbert space of the ground state of the full chain. Since this operator is constructed as the limit of a sequence of observables, the representation itself is, in principle, experimentally observable. We claim that the corresponding unitary representation of G is closely related to the representation found at the boundary of half-infinite chains. We conclude with determining the precise relation between the two representations for the class of frustration-free models with matrix product ground states.