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Quantum Glassiness and Topological Overprotection. Claudio Chamon. Collaborators: Claudio Castelnovo (BU), Christopher Mudry (PSI), Pierre Pujol (ENS-Lyon). PRL 05, cond-mat/0404182 PRB 04, cond-mat/0310710 PRB 05, cond-mat/0410562 Annal of Phys. 05, /0502068. DMR 0305482.

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Quantum Glassiness


Topological Overprotection

Claudio Chamon

Collaborators: Claudio Castelnovo (BU), Christopher Mudry (PSI), Pierre Pujol (ENS-Lyon)

PRL 05, cond-mat/0404182

PRB 04, cond-mat/0310710

PRB 05, cond-mat/0410562

Annal of Phys. 05, /0502068

DMR 0305482

Classical glassiness


Source: JOM, 52 (7) (2000)

Quantum glassy systems

disordered systems

eg. quantum spin glasses

extensions of

classical systems

Bray & Moore, J. Phys. C (1980)

Read, Sachdev, and Ye, PRB (1995)

frustrated systems

eg. 1 frustrated Josephson junctions

with long-range interactions

eg. II self-generated mean-field glasses

Kagan, Feigel'man, and Ioffe, ZETF/JETP (1999)

Westfahl, Schmalian, and Wolynes, PRB (2003)

Does one need an order parameter?

Does one need a thermodynamic or quantum phase transition?

Why not simply remain in a mixed state and not reach the ground state instead!?

Does the classical glassy state need to be a phase?

Does one need a phase transition?


Kinetic constraints can lead to slow relaxation even in classical paramagnets!

Ritort & Sollich - review of kinetic constrained classical models

What about quantum systems?

Not free to toy with the dynamics - it is given.

Where to look: systems with hard constraints: ice models, dimer models, loop models,...

Some clean strongly correlated systems with

topological order and fractionalization

Strong correlations that can lead to these exotic quantum spectral properties can in some instances also impose kinetic constraints, similar to those studied in the context of classical glass formers.


A solvable toy model

Why solvable examples are useful?

Classical glasses can be efficiently simulated in a computer; but real time simulation of a quantum system is doomed by oscillating phases (as bad as, if not worse, than the fermion sign problem)!

Even a quantum computer does not help; quantum computers are good for unitary evolution. One needs a “quantum supercomputer”, with many qubits dedicated to simulate the bath.

Solvable toy model can show unambiguously and without arbitrary or questionable approximations that there are quantum many body systems without disorder and with only local interactions that are incapable of reaching their quantum ground states.

2D example

(not glassy yet)

Kitaev, Ann. Phys. (2003) - quant-phys/97

Wen, PRL (2003)

topological order for quantum computing

Plaquettes with :


Same spectrum as free spins in a magnetic field


Ground state degeneracy

ground state:

on a torus:


two constraints:

4 ground states

Is the ground state reached?

bath of quantum oscillators;

acts on physical degrees of freedom

Caldeira & Leggett, Ann. Phys. (1983)

defects cannot simply be annihilated; plaquettes are flipped in multiplets

Is the ground state reached?

defects must go away

equilibrium concentration:

defects cannot be annihilated;

must be recombined

simple defect diffusion (escapes glassiness)

(Arrhenius law)

activated diffusion

Garrahan & Chandler, PNAS (2003)

Buhot & Garrahan, PRL (2002)

equivalent to classical glass model by

3D strong glass model

ground state


3D strong glass model

always flip 4 octahedra: never simple defect diffusion

(Arrhenius law)

What about quantum tunneling?

defect separation:

virtual process:

topological quantum protection

quantum OVER protection


Beyond the toy model...

Josephson junction arrays

of T-breaking superconductors


Constrained Ising model


Moore & Lee, cond-mat/0309717

Castelnovo, Pujol, and Chamon, PRB (2004)

Quantum model

Loop updates

ferro GS

Spin Ice

Dy2Ti2O7 (Ho2Ti2O7)

Snyder et al, Nature (2001)

Source: Snyder et al, Nature (2001)


Presented solvable examples of quantum many-body Hamiltonians of systems with exotic spectral properties (topological order and fractionalization) that are unable to reach their ground states as the environment temperature is lowered to absolute zero - systems remain in a mixed state down to T=0.

New constraint for topological quantum computing: that the ground state degeneracy is protected while the system is still able to reach the ground states.

Out-of-equilibrium strongly correlated quantum systems is an open frontier!