Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes

Journal Article · Sat Jan 15 00:00:00 EST 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2010.10.009· OSTI ID:21579837

Yoshida, Beni ^[1]

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1. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)

Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and the lack of a general framework for classifications. While frustration-free Hamiltonians, which appear as fixed point Hamiltonians of renormalization group transformations, may serve as representatives of quantum phases, it is still difficult to analyze and classify quantum phases of arbitrary frustration-free Hamiltonians exhaustively. Here, we address these problems by sharpening our considerations to a certain subclass of frustration-free Hamiltonians, called stabilizer Hamiltonians, which have been actively studied in quantum information science. We propose a model of frustration-free Hamiltonians which covers a large class of physically realistic stabilizer Hamiltonians, constrained to only three physical conditions; the locality of interaction terms, translation symmetries and scale symmetries, meaning that the number of ground states does not grow with the system size. We show that quantum phases arising in two-dimensional models can be classified exactly through certain quantum coding theoretical operators, called logical operators, by proving that two models with topologically distinct shapes of logical operators are always separated by quantum phase transitions.

• OSTI ID: 21579837
• Journal Information: Annals of Physics (New York), Vol. 326, Issue 1; Other Information: DOI: 10.1016/j.aop.2010.10.009; PII: S0003-4916(10)00186-7; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EXACT SOLUTIONS
GROUND STATES
HAMILTONIANS
INTERACTIONS
LOCALITY
MANY-BODY PROBLEM
PHASE TRANSFORMATIONS
QUANTUM INFORMATION
RENORMALIZATION
SYMMETRY
TOPOLOGY
TRANSFORMATIONS
TWO-DIMENSIONAL CALCULATIONS
ENERGY LEVELS
INFORMATION
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
MATHEMATICS
QUANTUM OPERATORS