arXiv subjects

J. E. Gubernatis

Publications and source records attributed to J. E. Gubernatis.

At least 37 records · Page 2Linked to original sources

arXiv2001

Simulating Physical Phenomena by Quantum Networks

Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by means of the algebra generated by the usual fermionic creation and annihilation operators, or by using the algebra of Pauli (spin-1/2) operators. The correspondence between the two algebras is given by the Jordan-Wigner isomorphism. As we previously noted similar one-to-one mappings enable one to represent any physical system in a quantum computer. In this paper we evolve and exploit this fundamental concept in quantum information processing to simulate generic physical phenomena by quantum networks. We give quantum circuits useful for the efficient evaluation of the physical properties (e.g, spectrum of observables or relevant correlation functions) of an arbitrary system with Hamiltonian $H$.

quant-ph↗

arXiv2001

Itinerant Ferromagnetism for Mixed Valence Systems

We introduce a novel mechanism for the unusual itinerant ferromagnetism found in mixed valence systems like Ce(Rh$_{1-x}$Ru$_x$)$_3$B$_2$, La$_x$Ce$_{1-x}$Rh$_3$B$_2$, US, USe, and UTe. With it we can provide an explanation for the long-unexplained large value of $T_c$ ($\sim$ 100$^\circ$K) value and the maximum in the magnetization below $T_c$ found experimentally. We also show that this novel itinerent ferromagnetism can be continuously connected with the localized case for which the energy scale is much smaller ($J_{RKKY} \sim$ 1$^\circ$K).

cond-mat.str-el↗

arXiv2000

Quantum Algorithms for Fermionic Simulations

We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to be of exponential complexity into one of polynomial complexity. The key to our demonstration is the spin-particle connection (or generalized Jordan-Wigner transformation) that allows exact algebraic invertible mappings of operators with different statistical properties. We give an explicit implementation of a simple problem using a quantum computer based on standard qubits.

cond-mat↗

arXiv2000

Pairing, Charge, and Spin Correlations in the Three-Band Hubbard Model

Using the Constrained Path Monte Carlo (CPMC) method, we simulated the two-dimensional, three-band Hubbard model to study pairing, charge, and spin correlations as a function of electron and hole doping and the Coulomb repulsion $V_{pd}$ between charges on neighboring Cu and O lattice sites. As a function of distance, both the $d_{x^2 - y^2}$-wave and extended s-wave pairing correlations decayed quickly. In the charge-transfer regime, increasing $V_{pd}$ decreased the long-range part of the correlation functions in both channels, while in the mixed-valent regime, it increased the long-range part of the s-wave behavior but decreased that of the d-wave behavior. Still the d-wave behavior dominated. At a given doping, increasing $V_{pd}$ increased the spin-spin correlations in the charge-transfer regime but decreased them in the mixed-valent regime. Also increasing $V_{pd}$ suppressed the charge-charge correlations between neighboring Cu and O sites. Electron and hole doping away from half-filling was accompanied by a rapid suppression of anti-ferromagnetic correlations.

cond-mat.str-el↗

arXiv2000

Ferromagnetism in the Two-Dimensional Periodic Anderson Model

Using the constrained-path Monte Carlo method, we studied the magnetic properties of the two-dimensional periodic Anderson model for electron fillings between 1/4 and 1/2. We also derived two effective low energy theories to assist in interpreting the numerical results. For 1/4 filling we found that the system can be a Mott or a charge transfer insulator, depending on the relative values of the Coulomb interaction and the charge transfer gap between the two non-interacting bands. The insulator may be a paramagnet or antiferromagnet. We concentrated on the effect of electron doping on these insulating phases. Upon doping we obtained a partially saturated ferromagnetic phase for low concentrations of conduction electrons. If the system were a charge transfer insulator, we would find that the ferromagnetism is induced by the well-known RKKY interaction. However, we found a novel correlated hopping mechanism inducing the ferromagnetism in the region where the non-doped system is a Mott insulator. Our regions of ferromagnetism spanned a much smaller doping range than suggested by recent slave boson and dynamical mean field theory calculations, but they were consistent with that obtained by density matrix renormalization group calculations of the one-dimensional periodic Anderson model.

cond-mat.str-el↗

arXiv2000

Random Walk Beyond Hartree-Fock

We give a brief discussion of the recently developed Constrained-Path Monte Carlo Method. This method is a quantum Monte Carlo technique that eliminates the fermion sign problem plaguing simulations of systems of interacting electrons. The elimination is accomplished by trading an exact procedure for an approximate one that has been demonstrated to give very accurate estimates of energies and many-body correlation functions. We also give a short review of its applications, a discussion of several strategies for parallelizing it, and some speculation of its future extensions.

cond-mat.str-el↗

arXiv1999

Study of Pairing Correlations in the Attractive Hubbard Model on Chains, Ladders, and Squares

We report the results of zero temperature quantum Monte Carlo simulations and zero temperature mean-field calculations of the attractive Hubbard model on chains, ladders, and square lattices. We investigated the predictability of the BCS approximation, the dimensional cross-over of the pairing correlation function from one to two dimensions as a function of the ladder width, and the scaling of these correlations to the thermodynamic limit of the two-dimensional model. We found that the BCS wave function is quantitatively correct only for small values of $U/t$. For the system sizes, electron fillings, and interaction strengths studied, we never saw the dimensional cross-over. In general our ability to achieve the dimensional cross-over and accurate scaling to the thermodynamic limit was limited by the size of the systems we could simulate. For these sizes, although we saw the necessary signature of ODLRO, the properties of the model did not vary monotonically with increasing system size because of shell effects. We contrast this situation with the dimensional cross-over and scaling to the thermodynamic limit of the Ising model.

cond-mat↗

arXiv1999

Issues and Observations on Applications of the Constrained-Path Monte Carlo Method to Many-Fermion Systems

We report several important observations that underscore the distinctions between the constrained-path Monte Carlo method and the continuum and lattice versions of the fixed-node method. The main distinctions stem from the differences in the state space in which the random walk occurs and in the manner in which the random walkers are constrained. One consequence is that in the constrained-path method the so-called mixed estimator for the energy is not an upper bound to the exact energy, as previously claimed. Several ways of producing an energy upper bound are given, and relevant methodological aspects are illustrated with simple examples.

cond-mat↗

arXiv1998

Correlated Wave-Functions and the Absence of Long Range Order in Numerical Studies of the Hubbard Model

We present a formulation of the Constrained Path Monte Carlo (CPMC) method for fermions that uses trial wave-functions that include many-body effects. This new formulation allows us to implement a whole family of generalized mean-field states as constraints. As an example, we calculated superconducting pairing correlation functions for the two-dimensional repulsive Hubbard model using a BCS trial state as the constraint. We compared the results with the case where a free-electron trial wave-function is used. We found that the correlation functions are independent of which state is used as the constraint, which reaffirms the results previously found by Zhang et. al regarding the suppression of long range pairing correlations as the system size increases.

cond-mat.supr-con↗

arXiv1998

Effects of doping on spin correlations in the periodic Anderson model

We studied the effects of hole doping on spin correlations in the periodic Anderson model, mainly at the full and three-quarters-full lower bands cases. In the full lower band case, strong anti-ferromagnetic correlations develop when the on-site repulsive interaction strength $U$ becomes comparable to the quasi-particle band width. In the three-quarters full case, a novel kind of spin correlation develops that is consistent with the resonance between a $(π,0)$ and a $(0,π)$ spin-density wave. In this state the spins on different sublattices appear uncorrelated. Hole doping away from the completely full case rapidly destroys the long-range anti-ferromagnetic correlations, in a manner reminiscent of the destruction of anti-ferromagnetism in the Hubbard model. In contrast to the Hubbard model, the doping does not shift the peak in the magnetic structure factor from the $(π,π)$ position. At dopings intermediate to the full and three-quarters full cases, only weak spin correlations exist.

cond-mat.str-el↗

arXiv1997

Stripes in a three-chain Hubbard ladder: a comparison of density-matrix renormalization group and constrained-path Monte Carlo results

Using both the density-matrix renormalization group method and the constrained-path quantum Monte Carlo method, we have studied the ground-state energies and the spin and hole densities of a $12 \times 3$ Hubbard model with open boundary conditions and 6 holes doped away from half-filling. Results obtained with these two methods agree well in the small and intermediate $U$ regimes. For $U/t \geq 6$ we find a ground-state with stripes.

cond-mat.str-el↗

arXiv1997

Quantum Monte Carlo Study of Hole Binding and Pairing Correlations in the Three-Band Hubbard Model

We simulated the 3-band Hubbard model using the Constrained Path Monte Carlo (CPMC) method in search for a possible superconducting ground state. The CPMC is a ground state method which is free of the exponential scaling of computing time with system size. We calculated the binding energy of a pair of holes for systems up to $6 \times 4$ unit cells. We also studied the pairing correlation functions versus distance for both the d-wave and extended s-wave channels in systems up to $6 \times 6$. We found that holes bind for a wide range of parameters and that the binding increased as the system size is increased. However, the pairing correlation functions decay quickly with distance. For the extended s channel, we found that as the Coulomb interaction $U_d$ on the Cu sites is increased, the long-range part of the correlation functions is suppressed and fluctuates around zero. For the $d_{x^2 - y^2}$ channel, we found that the correlations decay rapidly with distance towards a small positive value. However, this value becomes smaller as the interaction $U_d$ or the system size is increased.

cond-mat.supr-con↗

arXiv1997

Pairing Correlations in the Two-Dimensional Hubbard Model

We present the results of a quantum Monte Carlo study of the extended $s$ and the $d_{x^2-y^2}$ pairing correlation functions for the two-dimensional Hubbard model, computed with the constrained-path method. For small lattice sizes and weak interactions, we find that the $d_{x^2-y^2}$ pairing correlations are stronger than the extended $s$ pairing correlations and are positive when the pair separation exceeds several lattice constants. As the system size or the interaction strength increases, the magnitude of the long-range part of both correlation functions vanishes.

cond-mat.str-el↗

arXiv1996

A Constrained Path Monte Carlo Method for Fermion Ground States

We describe and discuss a recently proposed quantum Monte Carlo algorithm to compute the ground-state properties of various systems of interacting fermions. In this method, the ground state is projected from an initial wave function by a branching random walk in an over-complete basis of Slater determinants. By constraining the determinants according to a trial wave function $|ψ_T\rangle$, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if $|ψ_T\rangle$ is exact. We illustrate the method by describing in detail its implementation for the two-dimensional one-band Hubbard model. We show results for lattice sizes up to $16\times 16$ and for various electron fillings and interaction strengths. Besides highly accurate estimates of the ground-state energy, we find that the method also yields reliable estimates of other ground-state observables, such as superconducting pairing correlation functions. We conclude by discussing possible extensions of the algorithm.

cond-mat↗

arXiv1995

Real-Time Dynamics from Imaginary-Time Quantum Monte Carlo Simulations: Tests on Oscillator Chains

We used methods of Bayesian statistical inference and the principle of maximum entropy to analytically continue imaginary-time Green's function generated in quantum Monte Carlo simulations to obtain the real-time Green's functions. For test problems, we considered chains of harmonic and anharmonic oscillators whose properties we simulated by a hybrid path-integral quantum Monte Carlo method. From the imaginary-time displacement-displacement Green's function, we first obtained its spectral density. For harmonic oscillators, we demonstrated the peaks of this function were in the correct position and their area satisfied a sum rule. Additionally, as a function of wavenumber, the peak positions followed the correct dispersion relation. For a double-well oscillator, we demonstrated the peak location correctly predicted the tunnel splitting. Transforming the spectral densities to real-time Green's functions, we conclude that we can predict the real-time dynamics for length of times corresponding to 5 to 10 times the natural period of the model. The length of time was limited by an overbroadening of the peaks in the spectral density caused by the simulation algorithm.

cond-mat↗

arXiv1995

A Constrained Path Quantum Monte Carlo Method for Fermion Ground States

We propose a new quantum Monte Carlo algorithm to compute fermion ground-state properties. The ground state is projected from an initial wavefunction by a branching random walk in an over-complete basis space of Slater determinants. By constraining the determinants according to a trial wavefunction $|Ψ_T \rangle$, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if $|Ψ_T\rangle$ is exact. We report results on the two-dimensional Hubbard model up to size $16\times 16$, for various electron fillings and interaction strengths.

cond-mat↗

arXiv1995

Generalization of the Fortuin-Kasteleyn transformation and its application to quantum spin simulations,

We generalize the Fortuin-Kasteleyn (FK) cluster representation of the partition function of the Ising model to represent the partition function of quantum spin models with an arbitrary spin magnitude in arbitrary dimensions. This generalized representation enables us to develop a new cluster algorithm for the simulation of quantum spin systems by the worldline Monte Carlo method. Because the Swendsen-Wang algorithm is based on the FK representation, the new cluster algorithm naturally includes it as a special case. As well as the general description of the new representation, we present an illustration of our new algorithm for some special interesting cases: the Ising model, the antiferromagnetic Heisenberg model with $S=1$, and a general Heisenberg model. The new algorithm is applicable to models with any range of the exchange interaction, any lattice geometry, and any dimensions.

cond-mat↗

arXiv1994

Dual Monte Carlo and Cluster Algorithms

We discuss the development of cluster algorithms from the viewpoint of probability theory and not from the usual viewpoint of a particular model. By using the perspective of probability theory, we detail the nature of a cluster algorithm, make explicit the assumptions embodied in all clusters of which we are aware, and define the construction of free cluster algorithms. We also illustrate these procedures by rederiving the Swendsen-Wang algorithm, presenting the details of the loop algorithm for a worldline simulation of a quantum $S=$ 1/2 model, and proposing a free cluster version of the Swendsen-Wang replica method for the random Ising model. How the principle of maximum entropy might be used to aid the construction of cluster algorithms is also discussed.

cond-mat↗