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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 more recently machine learning and neural networks.
With these and related methods, my group explores the 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


  • Herzberg Medal Canadian Association of Physicists
  • 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

  • Ipsita Mandal, Stephen Inglis, Roger G. Melko Geometrical mutual information at the tricritical point of the two-dimensional Blume-Capel model J. Stat. Mech. (2016) 073105 arXiv: 1604.02464
  • C. M. Herdman, P.-N. Roy, R. G. Melko, A. Del Maestro Spatial entanglement entropy in the ground state of the Lieb-Liniger model Phys. Rev. B (in press) arXiv: 1606.03396
  • Johannes Helmes, Lauren E. Hayward Sierens, Anushya Chandran, William Witczak-Krempa, Roger G. Melko Universal corner entanglement of Dirac fermions and gapless bosons from the continuum to the lattice Phys. Rev. B (in press) arXiv: 1606.03096
  • S. A. Owerre, A. A. Burkov, Roger G. Melko A Large-S Study of Quantum Kagome Ice Phys. Rev. B 93, 144402 (2016) arXiv: 1512.03930
  • R. G. Melko, C. M. Herdman, D. Iouchtchenko, P.-N. Roy, A. Del Maestro Entangling qubit registers via many-body states of ultra cold atoms Phys. Rev. A 93, 042336 (2016) arXiv: 1512.06462
  • Yuan Wan, Juan Carrasquilla, Roger G. Melko Spinon walk in quantum spin ice Phys. Rev. Lett. 116, 167202 (2016) arXiv: 1510.00979
  • Sharmistha Sahoo, E. Miles Stoudenmire, Jean-Marie Stéphan, Trithep Devakul, Rajiv R. P. Singh, Roger G. Melko Unusual Corrections to Scaling and Convergence of Universal Renyi Properties at Quantum Critical Points Phys. Rev. B 93, 085120 (2016) arXiv: 1509.00468
  • Laimei Nie, Lauren E. Hayward Sierens, Roger G. Melko, Subir Sachdev, Steven A. Kivelson Fluctuating orders and quenched randomness in the cuprates Phys. Rev. B 92, 174505 (2015) http://arxiv.org/abs/1505.06206
  • B. Kulchytskyy, C. M. Herdman, Stephen Inglis, Roger G. Melko Detecting Goldstone Modes with Entanglement Entropy Phys. Rev. B 92, 115146 (2015) http://arxiv.org/abs/1502.01722
  • 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 http://arxiv.org/abs/1403.4258
  • Juan Carrasquilla, Zhihao Hao and Roger G. Melko A two-dimensional spin liquid in quantum kagome ice Nature Communications 6, Article number: 7421 http://arxiv.org/abs/1407.0037
  • 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 http://arxiv.org/abs/1409.6327
  • Zhihao Hao,Stephen Inglis and Roger Melko Destroying a topological quantum bit by condensing Ising vortices Nature Communications 5, Article number: 5781 http://arxiv.org/abs/1403.3982
  • 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) http://arxiv.org/abs/1406.2694
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • Leilee Chojnacki, Caleb Q. Cook, Denis Dalidovich, Lauren E. Hayward Sierens, Étienne Lantagne-Hurtubise, Roger G. Melko, Tiffany J. Vlaar Shape dependence of two-cylinder Renyi entropies for free bosons on a lattice arXiv: 1607.05311
  • Giacomo Torlai, Roger G. Melko Learning Thermodynamics with Boltzmann Machines arXiv: 1606.02718
  • Juan Carrasquilla, Roger G. Melko Machine learning phases of matter arXiv: 1605.01735
  • William Witczak-Krempa, Lauren E. Hayward Sierens, Roger G. Melko Cornering gapless quantum states via their torus entanglement arXiv: 1603.02684
  • Mohammad H. Amin, Evgeny Andriyash, Jason Rolfe, Bohdan Kulchytskyy, Roger Melko Quantum Boltzmann Machine arXiv: 1601.02036
  • Julia Wildeboer, Alexander Seidel, Roger G. Melko Entanglement Entropy and Topological Order in Resonating Valence-Bond Quantum Spin Liquids arXiv: 1510.07682
  • 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


  • Boulder Summer School for Condensed Matter and Materials Physics Topological Phases of Quantum Matter Boulder, CO
  • Quantum Computing: State of the Science, and the Future Scotiabank, Toronto
  • Computational Quantum Matter Summer School Sherbrooke
  • Entanglement Matters, Aspen summer workshop
  • Plenary speaker, Canadian Association of Physicists Congress, Ottawa ON
  • Colloquium: The Information Age in Simulations of Condensed Matter Northwestern University
  • From Quantum Field Theories to Numerical Methods, NORDITA Sweden
  • Turning the corner on Entanglement Entropy Oxford, UK
  • Entanglement and its role in many-body physics, CSSQI 2015: Canadian Summer School on Quantum Information The Bahen Center, University of Toronto
  • Tanglin' with Entanglement KITP public lecture (Friends of KITP) http://online.kitp.ucsb.edu/online/friends/melko/
  • Entanglement entropy and broken continuous symmetry Entanglement in Strongly Correlated Quantum Matter, KITP http://online.kitp.ucsb.edu/online/entangled15/metlitski/options.html
  • Quantum Monte Carlo, Dynamics, and Entanglement, D-wave Systems, Vancouver
  • The Numerical Linked Cluster Expansion & Entanglement at QCPs, Microsoft Research, Redmond
  • Entanglement Entropy at Strongly-Interacting Critical Points, Seminar, Sherbrooke
  • Collaboration on the Many Electron Problem, Simons Foundation, New York
  • Numerical and analytical methods for strongly correlated systems, Benasque, Spain
  • Computational Methods for Quantum Materials, Sherbrooke, Quebec