Physics – Quantum Physics
Scientific paper
2010-07-27
Annals of Physics 326, (2011) 15-95
Physics
Quantum Physics
81 pages, 30 figures, reference added
Scientific paper
10.1016/j.aop.2010.10.009
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.
No associations
LandOfFree
Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-320153