Steven R. White

Bio: Steven R. White is an academic researcher from University of Chicago. The author has contributed to research in topics: Density matrix renormalization group & Hubbard model. The author has an hindex of 77, co-authored 412 publications receiving 27496 citations. Previous affiliations of Steven R. White include Cornell University & Queen's University Belfast.

Density matrix formulation for quantum renormalization groups

Abstract: A generalization of the numerical renormalization-group procedure used first by Wilson for the Kondo problem is presented. It is shown that this formulation is optimal in a certain sense. As a demonstration of the effectiveness of this approach, results from numerical real-space renormalization-group calculations for Heisenberg chains are presented.

Density-matrix algorithms for quantum renormalization groups.

Abstract: A formulation of numerical real-space renormalization groups for quantum many-body problems is presented and several algorithms utilizing this formulation are outlined. The methods are presented and demonstrated using S=1/2 and S=1 Heisenberg chains as test cases. The key idea of the formulation is that rather than keep the lowest-lying eigenstates of the Hamiltonian in forming a new effective Hamiltonian of a block of sites, one should keep the most significant eigenstates of the block density matrix, obtained from diagonalizing the Hamiltonian of a larger section of the lattice which includes the block. This approach is much more accurate than the standard approach; for example, energies for the S=1 Heisenberg chain can be obtained to an accuracy of at least ${10}^{\mathrm{\ensuremath{-}}9}$. The method can be applied to almost any one-dimensional quantum lattice system, and can provide a wide variety of static properties.

Real-time evolution using the density matrix renormalization group.

Abstract: We describe an extension to the density matrix renormalization group method incorporating real-time evolution. Its application to transport problems in systems out of equilibrium and frequency dependent correlation functions is discussed and illustrated in several examples. We simulate a scattering process in a spin chain which generates a spatially nonlocal entangled wave function.

Spin-Liquid Ground State of the S = 1/2 Kagome Heisenberg Antiferromagnet

Abstract: We use the density matrix renormalization group to perform accurate calculations of the ground state of the nearest-neighbor quantum spin S = 1/2 Heisenberg antiferromagnet on the kagome lattice. We study this model on numerous long cylinders with circumferences up to 12 lattice spacings. Through a combination of very-low-energy and small finite-size effects, our results provide strong evidence that, for the infinite two-dimensional system, the ground state of this model is a fully gapped spin liquid.

Sign problem in the numerical simulation of many-electron systems

Abstract: We discuss the problems that arise in the numerical simulation of many-electron systems when the measure of the functional integrals is not positive definite. We present theoretical arguments and numerical data which indicate that the expectation value of the sign of the measure decreases exponentially as the inverse temperature \ensuremath{\beta} increases, unless the measure is forced to be positive by an explicit symmetry. We therefore conclude that a recent proposal for dealing with the sign problem due to Sorella et al. Leads to an uncontrolled approximation. In the cases we have studied it is a good approximation for the ground-state energy, and we present a method for calculating the correction needed to make it exact. However, for some physical quantities, such as the d-wave pair field susceptibility, the neglect of signs can yield misleading results.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Phd by thesis

Abstract: Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Many-Body Physics with Ultracold Gases

Abstract: This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.