Equilibrium dynamics of entangled states near quantum critical points

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Equilibrium dynamics of entangled states near
quantum critical points
Physical Review Letters 78, 843 (1997) 78,
2220 (1997) 95, 187201 (2005).
Kedar Damle (TIFR, Mumbai)
Subir Sachdev (Harvard)
Peter Young (UCSC)
Talk online at http//sachdev.physics.harvard.edu
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Why study quantum phase transitions ?
gc
g

• Critical point is (often) a novel (entangled)
  state of matter without quasiparticle excitations
  

• Critical excitations control dynamics in the
  wide quantum-critical region at non-zero
  temperatures.

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I. Quantum Ising Chain
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Experimental realization
LiHoF4
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Weakly-coupled qubits
Ground state
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Weakly-coupled qubits
Quasiparticle pole
Three quasiparticle continuum
3D
Structure holds to all orders in 1/g
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Quantum mechanical S-matrix has a universal
form at low momenta (in one
dimension)
(-1)
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Strongly-coupled qubits
Ground states
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Strongly-coupled qubits
Two domain-wall continuum
2D
Structure holds to all orders in g
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Entangled states at g of order unity
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Critical coupling
No quasiparticles --- dissipative critical
continuum
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S. Sachdev and J. Ye, Phys. Rev. Lett. 69, 2411
(1992). S. Sachdev and A.P. Young, Phys. Rev.
Lett. 78, 2220 (1997).
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II. Quantum O(3) non-linear s model
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Quantum mechanical S-matrix has a universal
form at low momenta (in one
dimension)
(-1)
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t
x
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(x,t)
t
(0,0)
x
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III. Quantum sine-Gordon model
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Quantum mechanical S-matrix has a universal
form at low momenta (in one
dimension)
(-1)
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III. Quantum sine-Gordon model
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Conclusions

1. Large, entangled quantum systems close to
   equilibrium have an intrinsic relaxation rate
   independent of the strength of the coupling to a
   heat bath.
2. This relaxation rate has a universal form near
   interacting quantum critical points
3. In one-dimensional systems