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Phase Diagram of OneDimensional Bosons in Disordered Potential

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Title: Phase Diagram of OneDimensional Bosons in Disordered Potential


1
Phase Diagram of One-Dimensional Bosons in
Disordered Potential
Anatoli Polkovnikov, Boston University
Collaboration
Ehud Altman - Weizmann Yariv Kafri -
Technion Gil Refael - CalTech
2
Dirty Bosons
Bosonic atoms on disordered substrate
4He on Vycor Cold atoms on optical lattice Small
capacitance Josephson Junction arrays Granular
Superconductors
3
O(2) quantum rotor model
4
One dimension Clean limit
Mapped to classical XY model in 11 dimensions
Superfluid
Insulator
Kosterlitz-Thouless transition
y
Universal jump in stifness
K-1
5
Z. Hadzibabic et. al., Observation of the BKT
transition in 2D bosons, Nature (2006)
Jump in the correlation function exponent a is
related to the jump in the SF stiffness
see A.P., E. Altman, E. Demler, PNAS (2006)
Vortex proliferation
Fraction of images showing at least one
dislocation
6
No off-diagonal disorder
E. Altman, Y. Kafri, A.P., G. Refael, PRL (2004)
Real Space RG
( Spin chains Dasgupta Ma PRB 80, Fisher PRB
94, 95 )
Eliminate the largest coupling
Follow evolution of the distribution functions.
7
Possible phases
Superfluid
Clusters grow to size of chain with repeated
decimation
8
(No Transcript)
9
These equations describe Kosterlits-Thouless
transition (independently confirmed by
Monte-Carlo study K. G. Balabanyan, N. Prokof'ev,
and B. Svistunov, PRL, 2005)
10
Diagonal disorder is relevant!!!
Next step in our approach. Consider.
This is a closed subspace under the RG
transformation rules. This constraint still
preserves particle hole symmetry.
11
New decimation rule for half-integer sites
Create effective spin ½ site
UW
12
Four coupled RG equations f(?), g(b), ,
is an attractive fixed point (corresponding to
relevance of diagonal disorder)
13
Number of spin ½ sites is irrelevant near the
critical point!
  • The transition is governed by the same
    non-interacting critical point as in the integer
    case.
  • Spin ½ sites are (dangerously) irrelevant at the
    critical point.
  • Insulating phase is the random singlet insulator
    with infinite compressibility.

14
General story for arbitrary diagonal disorder.
  • The Sf-IN transition is governed by the
    non-interacting fixed point and it always belongs
    to KT universality class.
  • Disorder in chemical potential is dangerously
    irrelevant and does not affect critical
    properties of the transition as well as the SF
    phase.

f0
g0
15
  • Insulating phase strongly depends on the type of
    disorder.
  • Integer filling incompressible Mott glass
  • ½ - integer filling random singlet insulator
    with diverging compressibility
  • Generic case Bose glass with finite
    compressibility
  • We confirm earlier findings (Fisher et. al. 1989,
    Giamarchi and Schulz 1988) that there is a direct
    KT transition from SF to Bose glass in 1D, in
    particular,
  • In 1D the system restores dynamical symmetry z1.

G
Random-singlet insulator
g01/Log(1/J)
Bose glass
Mott glass
16
This talk in a nutshell.
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