Office Hours: Mondays, 3 PM - 4 PM; Wednesdays, 11 AM - 12 PM

## Research Interests:

Profssor Sandvik is a condensed-matter theorist specializing in computational research on interacting quantum many-body systems, in particular quantum spin systems. His research has two interrelated themes; (i) developing algorithms for simulations of complex model systems and (ii) using those methods to study collective phenomena such as quantum phase transitions. "Home Page":http://physics.bu.edu/~sandvik "Computational Physics Course page":http://physics.bu.edu/~py502

## Selected papers:

- 10/03/08 Scale-Renormalized Matrix-Product States for Correlated Quantum Systems
- 09/19/08 Quantum Monte Carlo Simulations of Bosonic and Fermionic Impurities in a Two-Dimensional Hard-Core Boson System
- 11/29/07 Variational Quantum Monte Carlo Simulations with Tensor-Network States
- 11/15/07 Emergence of U(1) Symmetry in the 3D XY Model with Zq Anisotropy
- 07/25/07 Valence Bond Solid Phases in a Cubic Antiferromagnet
- 07/13/07 Anomalous Curie Response of Impurities in Quantum-Critical Spin-1/2 Heisenberg Antiferromagnets
- 06/01/07 Evidence for Deconfined Quantum Criticality in a Two-Dimensional Heisenberg Model with Four-Spin Interactions
- 02/26/07 Universal Scaling of the Neel Temperature of Near-Quantum-Critical Quasi-Two-Dimensional Heisenberg Antiferromagnets

## Education:

M.Sc., 1989, "Åbo Akademi University":http://www.abo.fi/public/?setlanguage=en Ph.D., 1993, "University of California, Santa Barbara":http://www.ucsb.edu

## In the news:

- Graduate Students Lou and Wang Land ICAM Travel Awards
- Professors Kearns and Sandvik Named APS Fellows

## Research Descriptions:

### Computational studies of quantum phase transitions

A continuous ground state phase transition occurring in a quantum-mechanical many-particle system as a function of some system parameter is referred to as a quantum phase transition. At the quantum-critical point separating two different types of ground states, the quantum fluctuations play a role analogous to thermal fluctuations in a phase transition occurring at nonzero temperature. An important aspect of these transitions is that the critical fluctuations and the associated scaling behavior of the quantum-critical point influences the system not only in the close vicinity of the ground-state critical point itself, but also in a wide finite-temperature region surrounding it. While many quantum phase transitions can be understood in terms of a mapping of the quantum mechanical problem onto a classical statistical-mechanics problem with an additional dimension (corresponding to time), recent attention has been focused on exotic transitions which fall outside the classical framework and may be important in strongly-correlated electronic systems such as the high-Tc cuprate superconductors. Prof. Sandvik’s group uses quantum Monte Carlo techniques to explore such transitions in model systems, primarily quantum spin systems. The purpose of this research is to find and characterize various quantum phase transitions in an un-biased (non-approximate) way, in order to provide benchmarks and guidance to developing theories. The influence of disorder (randomness) on the nature of quantum phase transitions is also studied.

### Quantum Monte Carlo algorithms

Monte Carlo methods are powerful computational tools for studies of equilibrium properties of classical many-particle systems. Using a stochastic process for generating random configurations of the system degrees of freedom, such methods simulate thermal fluctuations, so that expectation values of physical observables of interest are directly obtained by averaging “measurements” on the configurations. In quantum mechanical systems (e.g., electrons in a metal or superconductor, localized electronic spins (magnetic moments) of a certain insulators, or atoms in a magnetic or optical trap), quantum fluctuations have to be taken into account as well, especially at low temperatures, and these pose a much greater challenge than thermal fluctuations alone. Several different quantum Monte Carlo techniques have been devised during the past three decades, but many challenges remain in developing efficient algorithms for reaching large system sizes and low temperatures, and extending the applicability to models that are currently intractable. Prof. Sandvik is the principal developer of a scheme known as Stochastic Series Expansion, which during the last few years has emerged as the quantum Monte Carlo method of choice for studies of several classes of spin and boson systems. Recently, the group has initiated a research program to develop algorithms for studying ground states of quantum spin systems in the so-called valence bond (singlet pair) basis. This approach shows great promise for studies of quantum phase transitions and may also be applicable to fermion and boson models.