PIRSA:22100135

The Complexity and (Un)Computability of Quantum Phase Transitions

APA

Watson, J. (2022). The Complexity and (Un)Computability of Quantum Phase Transitions. Perimeter Institute. https://pirsa.org/22100135

MLA

Watson, James. The Complexity and (Un)Computability of Quantum Phase Transitions. Perimeter Institute, Oct. 26, 2022, https://pirsa.org/22100135

BibTex

          @misc{ pirsa_22100135,
            doi = {10.48660/22100135},
            url = {https://pirsa.org/22100135},
            author = {Watson, James},
            keywords = {Quantum Information},
            language = {en},
            title = {The Complexity and (Un)Computability of Quantum Phase Transitions},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {oct},
            note = {PIRSA:22100135 see, \url{https://pirsa.org}}
          }
          

James Watson University of Maryland

Abstract

The phase diagram of a material is of central importance in describing the properties and behaviour of a condensed matter system. Indeed, the study of quantum phase transitions has formed a central part of 20th and 21st Century physics. We examine the complexity and computability of determining the phase diagram of a general Hamiltonian. We show that in the worst case it is uncomputable and in more restricted cases, where the Hamiltonian is “better behaved”, it remains computationally intractable even for a quantum computer. Finally, we take a look at the relations between the Renormalization Group and uncomputable Hamiltonians.

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