Christopher Varney | University of West Florida (original) (raw)

Uploads

Papers by Christopher Varney

We report large scale determinant quantum Monte Carlo calculations of the effective bandwidth, mo... more We report large scale determinant quantum Monte Carlo calculations of the effective bandwidth, momentum distribution, and magnetic correlations of the square lattice fermion Hubbard Hamiltonian at half-filling. The sharp Fermi surface of the noninteracting limit is significantly broadened by the electronic correlations but retains signatures of the approach to the edges of the first Brillouin zone as the density increases. Finite-size scaling of simulations on large lattices allows us to extract the interaction dependence of the antiferromagnetic order parameter, exhibiting its evolution from weak-coupling to the strong-coupling Heisenberg limit. Our lattices provide improved resolution of the Green’s function in momentum space, allowing a more quantitative comparison with time-of-flight optical lattice experiments.

We study strong correlation effects in topological insulators via the Lanczos algorithm, which we... more We study strong correlation effects in topological insulators via the Lanczos algorithm, which we utilize to calculate the exact many-particle ground-state wave function and its topological properties. We analyze the simple, noninteracting Haldane model on a honeycomb lattice with known topological properties and demonstrate that these properties are already evident in small clusters. Next, we consider interacting fermions by introducing repulsive nearest-neighbor interactions. A first-order quantum phase transition was discovered at finite interaction strength between the topological band insulator and a topologically trivial Mott insulating phase by use of the fidelity metric and the charge-density-wave structure factor. We construct the phase diagram at T=0 as a function of the interaction strength and the complex phase for the next-nearest-neighbor hoppings. Finally, we consider the Haldane model with interacting hard-core bosons, where no evidence for a topological phase is observed. An important general conclusion of our work is that despite the intrinsic nonlocality of topological phases their key topological properties manifest themselves already in small systems and therefore can be studied numerically via exact diagonalization and observed experimentally, e.g., with trapped ions and cold atoms in optical lattices.

Encouraged by the success of first-principles cluster expansion methods for large-scale modeling ... more Encouraged by the success of first-principles cluster expansion methods for large-scale modeling of cubic alloys, we are developing a mixed-space cluster expansion approach for hexagonal-close-packed alloys. Here we discuss an explicit strain model, an essential component of cluster expansion models for modeling precipitate formation. We illustrate the method for magnesium alloys containing calcium and yttrium, two common additives in magnesium alloys.

Using exact diagonalization calculations, we investigate the ground-state phase diagram of the ha... more Using exact diagonalization calculations, we investigate the ground-state phase diagram of the hard-core Bose–Hubbard–Haldane model on the honeycomb lattice. This allows us to probe the stability of the Bose-metal phase proposed in Varney et al (2011 Phys. Rev. Lett. 107 077201), against various changes in the originally studied Hamiltonian.

In this paper, we investigate signatures of topological phase transitions in interacting systems.... more In this paper, we investigate signatures of topological phase transitions in interacting systems. We show that the key signature is the existence of a topologically protected level crossing, which is robust and sharply defines the topological transition, even in finite-size systems. Spatial symmetries are argued to play a fundamental role in the selection of the boundary conditions to be used to locate topological transitions in finite systems. We discuss the theoretical implications of this result, and utilize exact diagonalization to demonstrate its manifestations in the Haldane-Fermi-Hubbard model. Our findings provide an efficient way to detect topological transitions in experiments and in numerical calculations that cannot access the ground-state wave function.

The existence of quantum spin liquids was first conjectured by Pomeranchuk some 70 years ago, who... more The existence of quantum spin liquids was first conjectured by Pomeranchuk some 70 years ago, who argued that frustration in simple antiferromagnetic theories could result in a Fermi-liquid-like state for spinon excitations. Here we show that a simple quantum spin model on a honeycomb lattice hosts the long sought-for Bose metal with a clearly identifiable Bose-surface. The complete phase diagram of the model is determined via exact diagonalization and is shown to include four distinct phases separated by three quantum phase transitions.

In this chapter, I will review two quantum Monte Carlo (QMC) methods for lattice fermions, the wo... more In this chapter, I will review two quantum Monte Carlo (QMC) methods for lattice fermions, the world-line [1] and determinantal [2] algorithms. It is assumed that the reader have a firm grasp of statistical mechanics [3–5] and classical Monte Carlo techniques (See Ref. 6, Chapter 1 of Ref. 7, and Chapter 2 of Ref. 8). Let us consider a Hubbard Hamiltonian with particle-hole symmetry:

The extended Hubbard Hamiltonian is a widely accepted model for uncovering the effects of strong ... more The extended Hubbard Hamiltonian is a widely accepted model for uncovering the effects of strong correlations on the phase diagram of low-dimensional systems, and a variety of theoretical techniques have been applied to it. In this paper the world-line quantum Monte Carlo method is used to study spin, charge, and bond order correlations of the one-dimensional extended Hubbard model in the presence of coupling to the lattice. A static alternating lattice distortion (the ionic Hubbard model) leads to enhanced charge density wave correlations at the expense of antiferromagnetic order. When the lattice degrees of freedom are dynamic (the Hubbard-Holstein model), we show that a similar effect occurs even though the charge asymmetry must arise spontaneously. Although the evolution of the total energy with lattice coupling is smooth, the individual components exhibit sharp crossovers at the phase boundaries. Finally, we observe a tendency for bond order in the region between the charge and spin density wave phases.

The study of ultracold optically trapped atoms has opened new vistas in the physics of correlated... more The study of ultracold optically trapped atoms has opened new vistas in the physics of correlated quantum systems. Much attention has now turned to mixtures of bosonic and fermionic atoms. A central puzzle is the disagreement between the experimental observation of a reduced bosonic visibility Vb, and quantum Monte Carlo (QMC) calculations which show Vb increasing. In this paper, we present QMC simulations which evaluate the density profiles and Vb of mixtures of bosons and fermions in one-dimensional optical lattices. We resolve the discrepancy between theory and experiment by identifying parameter regimes where Vb is reduced, and where it is increased. We present a simple qualitative picture of the different response to the fermion admixture in terms of the superfluid and Mott-insulating domains before and after the fermions are included. Finally, we show that Vb exhibits kinks which are tied to the domain evolution present in the pure case, and also additional structure arising from the formation of boson-fermion molecules, a prediction for future experiments.

The emergence of local phases in a trapped two-component Fermi gas in an optical lattice is studi... more The emergence of local phases in a trapped two-component Fermi gas in an optical lattice is studied using quantum Monte Carlo simulations. We treat temperatures that are comparable to or lower than those presently achievable in experiments and large enough systems that both magnetic and paired phases can be detected by inspection of the behavior of suitable short-range correlations. We use the latter to suggest the interaction strength and temperature range at which experimental observation of incipient magnetism and d-wave pairing are more likely and evaluate the relation between entropy and temperature in two-dimensional confined fermionic systems.

We demonstrate the possible formation of hierarchical mesophases of vortex matter in layered supe... more We demonstrate the possible formation of hierarchical mesophases of vortex matter in layered superconducting systems where there are variations of interlayer thicknesses and layers are made of different superconducting materials. We show that because inter-vortex forces feature multiple length scales in this case the magnetic response features the formation of mesophases such as clusters of vortex clusters, concentric vortex rings, vortex clusters in a ring, and vortex stripes in a cluster. PACS numbers: 74.25.Uv, 74.25.Dw, 74.45.+c Condensed matter physics has long been concerned with explaining phenomena that result from competing interactions, covering a wide variety of topics from soft condensed matter systems to magnetism and ultracold atoms (for a recent overview see e.g. ). The richest pattern forming systems are those with several length scales. For example, structure formation in systems with two-scale repulsive interactions is highly relevant in hard condensed matter systems [3, 4], nuclear matter , and in colloids and other soft condensed matter systems .

QUEST is a part of the SciDAC project on next generation multi-scale quantum simulation software ... more QUEST is a part of the SciDAC project on next generation multi-scale quantum simulation software for strongly correlated materials. It is a Fortran 90/95 package that implements the determinant quantum Monte Carlo (DQMC) method for simulation of magnetic, superconducting, and metal-insulator transitions in model Hamiltonians. In this paper, we show how QUEST is capable of treating lattices of unprecedentedly large sizes and how this can be fruitful in the study of the physics of trapped fermionic system, in the development of more efficient solvers for Dynamical Mean Field Theory (DMFT) and as a tool to test and, in the future, improve diagrammatic approaches such as the Parquet approximation. We will also present a range of synergistic activities on the development of stable and robust numerical algorithms and hybrid granularity parallelization scheme that combines algorithmic and implementation techniques to high-performance DQMC simulation. The work reported here is a key step forward in achieving the goals of our SciDAC project.

We demonstrate, by considering the triangular lattice spin-1/2 Heisenberg model, that Monte Carlo... more We demonstrate, by considering the triangular lattice spin-1/2 Heisenberg model, that Monte Carlo sampling of skeleton Feynman diagrams within the fermionization framework offers a universal first-principles tool for strongly correlated lattice quantum systems. We observe the fermionic sign blessing-cancellation of higher order diagrams leading to a finite convergence radius of the series. We calculate magnetic susceptibility of the triangular-lattice quantum antiferromagnet in the correlated paramagnet regime and reveal surprising-numerically exact-microscopic correspondence with its classical counterpart at all accessible temperatures. Extrapolation of the observed relation to zero temperature suggests the absence of the magnetic order in the ground state. We critically examine implications of this unusual scenario.

Using fermionic representation of spin degrees of freedom within the Popov-Fedotov approach we de... more Using fermionic representation of spin degrees of freedom within the Popov-Fedotov approach we develop an algorithm for Monte Carlo sampling of skeleton Feynman diagrams for Heisenberg type models. Our scheme works without modifications for any dimension of space, lattice geometry, and interaction range, i.e. it is suitable for dealing with frustrated magnetic systems at finite temperature. As a practical application we compute uniform magnetic susceptibility of the antiferromagnetic Heisenberg model on the triangular lattice and compare our results with the best available high-temperature expansions. We also report results for the momentum-dependence of the static magnetic susceptibility throughout the Brillouin zone.

We report large scale determinant quantum Monte Carlo calculations of the effective bandwidth, mo... more We report large scale determinant quantum Monte Carlo calculations of the effective bandwidth, momentum distribution, and magnetic correlations of the square lattice fermion Hubbard Hamiltonian at half-filling. The sharp Fermi surface of the noninteracting limit is significantly broadened by the electronic correlations but retains signatures of the approach to the edges of the first Brillouin zone as the density increases. Finite-size scaling of simulations on large lattices allows us to extract the interaction dependence of the antiferromagnetic order parameter, exhibiting its evolution from weak-coupling to the strong-coupling Heisenberg limit. Our lattices provide improved resolution of the Green’s function in momentum space, allowing a more quantitative comparison with time-of-flight optical lattice experiments.

We study strong correlation effects in topological insulators via the Lanczos algorithm, which we... more We study strong correlation effects in topological insulators via the Lanczos algorithm, which we utilize to calculate the exact many-particle ground-state wave function and its topological properties. We analyze the simple, noninteracting Haldane model on a honeycomb lattice with known topological properties and demonstrate that these properties are already evident in small clusters. Next, we consider interacting fermions by introducing repulsive nearest-neighbor interactions. A first-order quantum phase transition was discovered at finite interaction strength between the topological band insulator and a topologically trivial Mott insulating phase by use of the fidelity metric and the charge-density-wave structure factor. We construct the phase diagram at T=0 as a function of the interaction strength and the complex phase for the next-nearest-neighbor hoppings. Finally, we consider the Haldane model with interacting hard-core bosons, where no evidence for a topological phase is observed. An important general conclusion of our work is that despite the intrinsic nonlocality of topological phases their key topological properties manifest themselves already in small systems and therefore can be studied numerically via exact diagonalization and observed experimentally, e.g., with trapped ions and cold atoms in optical lattices.

Encouraged by the success of first-principles cluster expansion methods for large-scale modeling ... more Encouraged by the success of first-principles cluster expansion methods for large-scale modeling of cubic alloys, we are developing a mixed-space cluster expansion approach for hexagonal-close-packed alloys. Here we discuss an explicit strain model, an essential component of cluster expansion models for modeling precipitate formation. We illustrate the method for magnesium alloys containing calcium and yttrium, two common additives in magnesium alloys.

Using exact diagonalization calculations, we investigate the ground-state phase diagram of the ha... more Using exact diagonalization calculations, we investigate the ground-state phase diagram of the hard-core Bose–Hubbard–Haldane model on the honeycomb lattice. This allows us to probe the stability of the Bose-metal phase proposed in Varney et al (2011 Phys. Rev. Lett. 107 077201), against various changes in the originally studied Hamiltonian.

In this paper, we investigate signatures of topological phase transitions in interacting systems.... more In this paper, we investigate signatures of topological phase transitions in interacting systems. We show that the key signature is the existence of a topologically protected level crossing, which is robust and sharply defines the topological transition, even in finite-size systems. Spatial symmetries are argued to play a fundamental role in the selection of the boundary conditions to be used to locate topological transitions in finite systems. We discuss the theoretical implications of this result, and utilize exact diagonalization to demonstrate its manifestations in the Haldane-Fermi-Hubbard model. Our findings provide an efficient way to detect topological transitions in experiments and in numerical calculations that cannot access the ground-state wave function.

The existence of quantum spin liquids was first conjectured by Pomeranchuk some 70 years ago, who... more The existence of quantum spin liquids was first conjectured by Pomeranchuk some 70 years ago, who argued that frustration in simple antiferromagnetic theories could result in a Fermi-liquid-like state for spinon excitations. Here we show that a simple quantum spin model on a honeycomb lattice hosts the long sought-for Bose metal with a clearly identifiable Bose-surface. The complete phase diagram of the model is determined via exact diagonalization and is shown to include four distinct phases separated by three quantum phase transitions.

In this chapter, I will review two quantum Monte Carlo (QMC) methods for lattice fermions, the wo... more In this chapter, I will review two quantum Monte Carlo (QMC) methods for lattice fermions, the world-line [1] and determinantal [2] algorithms. It is assumed that the reader have a firm grasp of statistical mechanics [3–5] and classical Monte Carlo techniques (See Ref. 6, Chapter 1 of Ref. 7, and Chapter 2 of Ref. 8). Let us consider a Hubbard Hamiltonian with particle-hole symmetry:

The extended Hubbard Hamiltonian is a widely accepted model for uncovering the effects of strong ... more The extended Hubbard Hamiltonian is a widely accepted model for uncovering the effects of strong correlations on the phase diagram of low-dimensional systems, and a variety of theoretical techniques have been applied to it. In this paper the world-line quantum Monte Carlo method is used to study spin, charge, and bond order correlations of the one-dimensional extended Hubbard model in the presence of coupling to the lattice. A static alternating lattice distortion (the ionic Hubbard model) leads to enhanced charge density wave correlations at the expense of antiferromagnetic order. When the lattice degrees of freedom are dynamic (the Hubbard-Holstein model), we show that a similar effect occurs even though the charge asymmetry must arise spontaneously. Although the evolution of the total energy with lattice coupling is smooth, the individual components exhibit sharp crossovers at the phase boundaries. Finally, we observe a tendency for bond order in the region between the charge and spin density wave phases.

The study of ultracold optically trapped atoms has opened new vistas in the physics of correlated... more The study of ultracold optically trapped atoms has opened new vistas in the physics of correlated quantum systems. Much attention has now turned to mixtures of bosonic and fermionic atoms. A central puzzle is the disagreement between the experimental observation of a reduced bosonic visibility Vb, and quantum Monte Carlo (QMC) calculations which show Vb increasing. In this paper, we present QMC simulations which evaluate the density profiles and Vb of mixtures of bosons and fermions in one-dimensional optical lattices. We resolve the discrepancy between theory and experiment by identifying parameter regimes where Vb is reduced, and where it is increased. We present a simple qualitative picture of the different response to the fermion admixture in terms of the superfluid and Mott-insulating domains before and after the fermions are included. Finally, we show that Vb exhibits kinks which are tied to the domain evolution present in the pure case, and also additional structure arising from the formation of boson-fermion molecules, a prediction for future experiments.

The emergence of local phases in a trapped two-component Fermi gas in an optical lattice is studi... more The emergence of local phases in a trapped two-component Fermi gas in an optical lattice is studied using quantum Monte Carlo simulations. We treat temperatures that are comparable to or lower than those presently achievable in experiments and large enough systems that both magnetic and paired phases can be detected by inspection of the behavior of suitable short-range correlations. We use the latter to suggest the interaction strength and temperature range at which experimental observation of incipient magnetism and d-wave pairing are more likely and evaluate the relation between entropy and temperature in two-dimensional confined fermionic systems.

We demonstrate the possible formation of hierarchical mesophases of vortex matter in layered supe... more We demonstrate the possible formation of hierarchical mesophases of vortex matter in layered superconducting systems where there are variations of interlayer thicknesses and layers are made of different superconducting materials. We show that because inter-vortex forces feature multiple length scales in this case the magnetic response features the formation of mesophases such as clusters of vortex clusters, concentric vortex rings, vortex clusters in a ring, and vortex stripes in a cluster. PACS numbers: 74.25.Uv, 74.25.Dw, 74.45.+c Condensed matter physics has long been concerned with explaining phenomena that result from competing interactions, covering a wide variety of topics from soft condensed matter systems to magnetism and ultracold atoms (for a recent overview see e.g. ). The richest pattern forming systems are those with several length scales. For example, structure formation in systems with two-scale repulsive interactions is highly relevant in hard condensed matter systems [3, 4], nuclear matter , and in colloids and other soft condensed matter systems .

QUEST is a part of the SciDAC project on next generation multi-scale quantum simulation software ... more QUEST is a part of the SciDAC project on next generation multi-scale quantum simulation software for strongly correlated materials. It is a Fortran 90/95 package that implements the determinant quantum Monte Carlo (DQMC) method for simulation of magnetic, superconducting, and metal-insulator transitions in model Hamiltonians. In this paper, we show how QUEST is capable of treating lattices of unprecedentedly large sizes and how this can be fruitful in the study of the physics of trapped fermionic system, in the development of more efficient solvers for Dynamical Mean Field Theory (DMFT) and as a tool to test and, in the future, improve diagrammatic approaches such as the Parquet approximation. We will also present a range of synergistic activities on the development of stable and robust numerical algorithms and hybrid granularity parallelization scheme that combines algorithmic and implementation techniques to high-performance DQMC simulation. The work reported here is a key step forward in achieving the goals of our SciDAC project.

We demonstrate, by considering the triangular lattice spin-1/2 Heisenberg model, that Monte Carlo... more We demonstrate, by considering the triangular lattice spin-1/2 Heisenberg model, that Monte Carlo sampling of skeleton Feynman diagrams within the fermionization framework offers a universal first-principles tool for strongly correlated lattice quantum systems. We observe the fermionic sign blessing-cancellation of higher order diagrams leading to a finite convergence radius of the series. We calculate magnetic susceptibility of the triangular-lattice quantum antiferromagnet in the correlated paramagnet regime and reveal surprising-numerically exact-microscopic correspondence with its classical counterpart at all accessible temperatures. Extrapolation of the observed relation to zero temperature suggests the absence of the magnetic order in the ground state. We critically examine implications of this unusual scenario.

Using fermionic representation of spin degrees of freedom within the Popov-Fedotov approach we de... more Using fermionic representation of spin degrees of freedom within the Popov-Fedotov approach we develop an algorithm for Monte Carlo sampling of skeleton Feynman diagrams for Heisenberg type models. Our scheme works without modifications for any dimension of space, lattice geometry, and interaction range, i.e. it is suitable for dealing with frustrated magnetic systems at finite temperature. As a practical application we compute uniform magnetic susceptibility of the antiferromagnetic Heisenberg model on the triangular lattice and compare our results with the best available high-temperature expansions. We also report results for the momentum-dependence of the static magnetic susceptibility throughout the Brillouin zone.