Robust and fragile PT-symmetric phases in a tight-binding chain

Journal Article · Wed Sep 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.030103· OSTI ID:21448604

Joglekar, Yogesh N; Scott, Derek; Babbey, Mark; Saxena, Avadh ^[1]

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1. Department of Physics, Indiana University Purdue University Indianapolis (IUPUI), Indianapolis, Indiana 46202 (United States)

We study the phase diagram of a parity- and time-reversal- (PT-) symmetric tight-binding chain with N sites and hopping energy J in the presence of two impurities with imaginary potentials {+-}i{gamma} located at arbitrary (P-symmetric) positions (m,m-bar=N+1-m) on the chain where m{<=}N/2. We find that except in the two special cases where impurities are either the farthest or the closest, the PT-symmetric region is algebraically fragile. We analytically and numerically obtain the critical impurity potential {gamma}{sub PT} and show that {gamma}{sub PT{proportional_to}}1/N{yields}0 as N{yields}{infinity} except in the two special cases. When the PT symmetry is spontaneously broken, we find that the maximum number of complex eigenvalues is given by 2m. When the two impurities are the closest, we show that {gamma}{sub PT} in the limit N{yields}{infinity} approaches J (J/2) provided that N is even (odd). For an even N, the PT symmetry is maximally broken, whereas for an odd N, it is sequentially broken. Our results show that the phase diagram of a PT-symmetric tight-binding chain is extremely rich and that, in the continuum limit, this model may give rise to hitherto unexplored PT-symmetric Hamiltonians.

• OSTI ID: 21448604
• Journal Information: Physical Review. A, Vol. 82, Issue 3; Other Information: DOI: 10.1103/PhysRevA.82.030103; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
C INVARIANCE
EIGENVALUES
HAMILTONIANS
NUMERICAL SOLUTION
P INVARIANCE
PARITY
PHASE DIAGRAMS
POTENTIALS
SYMMETRY
T INVARIANCE
DIAGRAMS
INFORMATION
INVARIANCE PRINCIPLES
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
PARTICLE PROPERTIES
QUANTUM OPERATORS