Rare regions, ie, rare large spatial disorder fluctuations, can dramatically change the
properties of a phase transition in a quenched disordered system. In generic classical …

We discuss designer Hamiltonians—lattice models tailored to be free from sign problems
(“de-signed”) when simulated with quantum Monte Carlo (QMC) methods but which still host …

In the last decade, quantum simulators, and in particular cold atoms in optical lattices, have
emerged as a valuable tool to study strongly correlated quantum matter. These experiments …

NATURE abounds with phase transitions. The boiling and freezing of water are everyday
examples of phase transitions, as are more exotic processes such as superconductivity and …

These lecture notes introduce quantum spin systems and several computational methods for
studying their ground‐state and finite‐temperature properties. Symmetry‐breaking and …

Fermionic atoms in optical lattices have served as a useful model system in which to study
and emulate the physics of strongly correlated matter. Driven by the advances of high …

We introduce the concept of directed loops in stochastic series expansion and path-integral
quantum Monte Carlo methods. Using the detailed balance rules for directed loops, we …

The ground-state parameters of the two-dimensional S= 1/2 antiferromagnetic Heisenberg
model are calculated using the stochastic series expansion quantum Monte Carlo method …

I review two classes of strong coupling problems in condensed matter physics, and describe
insights gained by application of the AdS/CFT correspondence. The first class concerns non …

We have studied the phase diagram and excitations of the spin-orbital model derived for a
three-dimensional perovskite lattice, as in KCuF 3. The results demonstrate that the orbital …