Roger Melko

Roger Melko's picture
University of Waterloo - Department of Physics and Astronomy

Area of Research:
Phone: x8560

Research Interests

My group's interests involve strongly-correlated quantum many-body systems, with a focus on emergent phenomena, novel phases and phase transitions, quantum criticality, and entanglement. We emphasize computational methods as a theoretical technique, in particular the development of state-of-the-art algorithms for the study of strongly-interacting systems. Our work has employed Monte Carlo simulations, Density Matrix Renormalization Group, Series Expansions, and related methods, to explore low-temperature physics in quantum magnets, cold atoms in optical lattices, bosonic fluids, and models of topological quantum computers. I am particularly involved in studying microscopic models that display interesting quantum behavior in the bulk, such as superconducting, spin liquid, topological, superfluid or supersolid phases. We are also interested in broader ideas in computational physics, the development of efficient algorithms for simulating quantum mechanical systems on classical computers, and the relationship of these methods to the field of quantum information science.

Positions Held

  • 2007- Department of Physics and Astronomy, University of Waterloo Professor
  • 2005-2007 Oak Ridge National Laboratory, Tennessee Wigner Fellow


  • Young Scientist Prize in Computational Physics, International Union of Pure and Applied Physics (IUPAP), "for his innovative and deep achievements in developing quantum Monte Carlo methods for quantum information theory and condensed matter physics."
  • Early Researcher Award, Ontario Ministry of Research and Innovation

Recent Publications

  • Juan Carrasquilla, Zhihao Hao and Roger G. Melko A two-dimensional spin liquid in quantum kagome ice Nature Communications 6, Article number: 7421
  • Ryan V. Mishmash, Iván González, Roger G. Melko, Olexei I. Motrunich, and Matthew P. A. Fisher Continuous Mott transition between a metal and a quantum spin liquid Phys. Rev. B 91, 235140
  • E.M. Stoudenmire, Peter Gustainis, Ravi Johal, Stefan Wessel, Roger G. Melko Corner contribution to the entanglement entropy of strongly-interacting O(2) quantum critical systems in 2+1 dimensions Phys. Rev. B 90, 235106
  • Zhihao Hao,Stephen Inglis and Roger Melko Destroying a topological quantum bit by condensing Ising vortices Nature Communications 5, Article number: 5781
  • Lauren E. Hayward, Andrew J. Achkar, David G. Hawthorn, Roger G. Melko, Subir Sachdev Diamagnetism and density wave order in the pseudogap regime of YBa2Cu3O6+x Phys. Rev. B 90, 094515 (2014)
  • C. M. Herdman, Stephen Inglis, P.-N. Roy, R. G. Melko, A. Del Maestro A path integral Monte Carlo method for Rényi entanglement entropies Phys. Rev. E 90, 013308 (2014) arXiv: 1404.7104
  • Ann B. Kallin, E. M. Stoudenmire, Paul Fendley, Rajiv R. P. Singh, Roger G. Melko Corner contribution to the entanglement entropy of an O(3) quantum critical point in 2+1 dimensions J. Stat. Mech. (2014) P06009 arXiv: 1401.3504
  • C. M. Herdman, P.-N. Roy, R. G. Melko, A. Del Maestro Particle entanglement in continuum many-body systems via quantum Monte Carlo Phys. Rev. B 89, 140501 (2014) arXiv: 1310.8332
  • Jean-Marie Stéphan, Stephen Inglis, Paul Fendley, Roger G. Melko Geometric mutual information at classical critical points Phys. Rev. Lett. 112, 127204 (2014) arXiv: 1312.3954
  • Lauren E. Hayward, David G. Hawthorn, Roger G. Melko, Subir Sachdev Angular Fluctuations of a Multicomponent Order Describe the Pseudogap of YBa2Cu3O6+x Science 343, 1336 (2014) arXiv: 1309.6639
  • Matthew B. Hastings, Grant H. Watson, Roger G. Melko Self-Correcting Quantum Memories Beyond the Percolation Threshold Phys. Rev. Lett. 112, 070501 (2014) arXiv: 1309.2680
  • Matthew S. Block, Roger G. Melko, Ribhu K. Kaul Fate of CP(N-1) fixed points with q-monopoles Phys. Rev. Lett. 111, 137202 (2013) arXiv: 1307.0519
  • Stephen Inglis, Roger G. Melko, Entanglement at a Two-Dimensional Quantum Critical Point: a T=0 Projector Quantum Monte Carlo Study, New J. Phys. 15 073048 (2013) arxiv:cond-mat.str-el/1305.1069
  • Jason Iaconis, Stephen Inglis, Ann B. Kallin, and Roger G. Melko Detecting classical phase transitions with Renyi mutual information Phys. Rev. B 87, 195134 (2013) arXiv: 1210.2403
  • L. D. C. Jaubert, M. J. Harris, T. Fennell, R. G. Melko, S. T. Bramwell, and P. C. W. Holdsworth Topological-Sector Fluctuations and Curie-Law Crossover in Spin Ice Phys. Rev. X 3, 011014 - Published 21 February 2013 arXiv: 1204.6266
  • Ribhu K. Kaul, Roger G. Melko, Anders W. Sandvik Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations Annu. Rev. Con. Mat. Phys. 4, 179 (2013) arXiv: 1204.5405
  • Jean-Marie Stéphan, Hyejin Ju, Paul Fendley and Roger G Melko Entanglement in gapless resonating-valence-bond states New J. Phys. 15 015004 (2013) arXiv: 1207.3820
  • Stephen Inglis and Roger G. Melko Wang-Landau method for calculating Rényi entropies in finite-temperature quantum Monte Carlo simulations Phys. Rev. E 87, 013306 - Published 22 January 2013 arXiv: 1207.5052
  • Ann B. Kallin, Katharine Hyatt, Rajiv R. P. Singh, Roger G. Melko, Entanglement at a Two-Dimensional Quantum Critical Point: a Numerical Linked Cluster Expansion Study, Phys. Rev. Lett. 110, 135702 (2013), arXiv: 1212.5269
  • Rajiv R. P. Singh, Roger G. Melko, and Jaan Oitmaa Thermodynamic singularities in the entanglement entropy at a two-dimensional quantum critical point Phys. Rev. B 86, 075106 - Published 6 August 2012 arXiv: 1204.1340
  • Laimei Nie, Lauren E. Hayward Sierens, Roger G. Melko, Subir Sachdev, Steven A. Kivelson Fluctuating orders and quenched randomness in the cuprates
  • B. Kulchytskyy, C. M. Herdman, Stephen Inglis, Roger G. Melko Detecting Goldstone Modes with Entanglement Entropy
  • Strongly Correlated Systems: Numerical Methods Chapter 7: Stochastic Series Expansion Quantum Monte Carlo By Roger Melko Springer Series in Solid-State Sciences Volume 176, 2013, pp 185-206


  • Entanglement and its role in many-body physics, CSSQI 2015: Canadian Summer School on Quantum Information The Bahen Center, University of Toronto
  • Entanglement entropy and broken continuous symmetry Entanglement in Strongly Correlated Quantum Matter, KITP
  • Tanglin' with Entanglement KITP public lecture (Friends of KITP)
  • The Numerical Linked Cluster Expansion & Entanglement at QCPs, Microsoft Research, Redmond
  • Quantum Monte Carlo, Dynamics, and Entanglement, D-wave Systems, Vancouver
  • Entanglement Entropy at Strongly-Interacting Critical Points, Seminar, Sherbrooke
  • Numerical and analytical methods for strongly correlated systems, Benasque, Spain
  • Collaboration on the Many Electron Problem, Simons Foundation, New York
  • Computational Methods for Quantum Materials, Sherbrooke, Quebec
  • Workshop: Field Theoretic Computer Simulations for Particle Physics and Condensed Matter, Boston University, Boston, MA
  • German DPG March Meeting Dresden, Germany
  • Seminar Ludwig-Maximilians-Universitat, Munich
  • Seminar, McGill University, Montreal
  • Aspen Winter Conference: Beyond Quasiparticles, New Paradigms for Quantum Fluids Aspen, Colorado
  • Colloquium University of Vermont, Burlington
  • Workshop on Statistical Physics of Quantum Matter, Taipei, Taiwan