Theory of the Quantum Critical Fluctuations in Cuprates

Abstract

The statistical mechanics of the time-reversal and inversion symmetry breaking order parameter, possibly observed in the pseudogap region of the phase diagram of the Cuprates, can be represented by the Ashkin-Teller model. We add kinetic energy and dissipation to the model for a quantum generalization and show that the correlations are determined by two sets of charges, one interacting locally in time and logarithmically in space and the other locally in space and logarithmically in time. The quantum critical fluctuations are derived and shown to be of the form postulated in 1989 to give the marginal fermi-liquid properties. The model solved and the methods devised are likely to be of interest also to other quantum phase transitions.

References in corpus (8)

• Magnetic order in the pseudogap phase of high-$T_C$ superconductors
• A Theory of the Pseudogap State of the Cuprates
• Singular Fermi Liquids
• Spontaneous time reversal symmetry breaking in the pseudogap state of high-Tc superconductors
• Detection and Implications of a Time-reversal breaking state in underdoped Cuprates
• Finite temperature properties of quantum Lifshitz transitions between valence bond solid phases: An example of `local' quantum criticality
• Floating phase in a dissipative Josephson junction array
• Dissipation, topology, and quantum phase transition in a one-dimensional Joesphson junction array

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