Quantum Monte Carlo Methods at Work for Novel Phases of Matter

Trieste, Italy, Jan 23 - Feb 3, 2012

**Anders W. Sandvik, Boston University**

In these lectures I discuss quantum Monte Carlo simulations of quantum spin systems. Finite-temperature (Lecture 1) and ground state (Lecture 2) methods are discussed in sufficient detail to understand the workings of the most efficient program implementations for S=1/2 Heisenberg antiferromagnetis and extensions including multi-spin interactions ("J-Q" models). The program implementations are further discussed and used in the afternoon tutorials (directed by Ying Tang). In the third lecture I discuss the quantum phase transition between a Neel antiferromagnet and a valence-bond-solid in the J-Q model; the best candidate so far for a "deconfined" quantum-critical point.

**Lecture slides **
SSE quantum Monte Carlo (Jan 30)
Projector Monte Carlo (Jan 31)
Animation: 1D VBS at J/Q=0
Animation: 1D VBS at J/Q=1/2
Animation: 1D VBS at (J/Q)c
Case study: Neel to valence-bond-solid transition in 2D (Feb 1)
Animation: 1D VBS with one spinon
Animation: 1D VBS with two spinons

Animation: Build-up of 2D VBS distribution

**Tutorials (instructor: Ying Tang, Boston University)**

**SSE QMC for S=1/2 Heisenberg model (Jan 30) **
Instructions (+ results added after)
Code: ssebasic.f90 (simulation program; output should be processed by 'sseres.f90')
Code: sseres.f90 (program to compute averages and error bars from output of ssebasic.f90)

**Projector QMC for S=1/2 Heisenberg model (Jan 31) **
Instructions (+ results added after)
Code: probasic.f90 (simulation program; output should be processed by 'prores.f90')
Code: prores.f90 (program to compute averages and error bars from output of probasic.f90)

**Projector QMC for J-Q3 chain (Jan 31) **
Instructions (+ results added after)
Code: jq3chain.f90 (simulation program; output should be processed by 'jq3res.f90')
Code: jq3res.f90 (program to compute averages and error bars from output of jq3chain.f90)

Some of this material is based upon work supported by the National Science Foundation (USA) under Grants DMR-0803510 and DMR-1104708. Any opinions, findings, and conclusions or recommendations expressed in this material a re those of the authors and do not necessarily reflect the views of the National Science Foundation