Purdue University Graduate School
Complexity near critical points.pdf (1.1 MB)

Complexity near critical points

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posted on 2023-09-15, 20:49 authored by Uday SoodUday Sood

Complexity has played an increasingly important role in recent years. In this dissertation, we study some notions of complexity in systems that exhibit critical behaviour. Our results show that complexity as it is generally understood in holographic and lattice models of criticality can have several ambiguities. But despite these ambiguities, there are some features that are universally true. On the phase diagram of the system, it is the critical point which has the most complex ground state. States of physical systems with a large complexity tend to be hard to simulate using quantum circuits. Near the critical point, there is a part of complexity which is non-analytic and scales universally, i.e, the scaling is independent of the microscopic details of the Hamiltonian but depends only on the dimensionality of the system, and of the deforming operator. The coefficient of this term is unambiguous, i.e, it is not affected by the various changes in the definition of complexity which plague all the analytic terms near the critical point. We show this in lattice, field-theoretic and holographic calculations. These results were first presented in our earlier studies.


Quantum Information in a strongly interacting quantum simulator: from gauge/string theory duality to analogue black holes

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An Experimental and Theoretical High Energy Physics Program

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Degree Type

  • Doctor of Philosophy


  • Physics and Astronomy

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Martin Kruczenski

Additional Committee Member 2

Sergei Khlebnikov

Additional Committee Member 3

Nima Lashkari

Additional Committee Member 4

Chen-Lung Hung