Fermi Liquid Singularities and Quantum Criticality or Influence of Generic Soft Modes on Quantum Critical Behavior

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Dietrich Belitz University of Oregon

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I. Fermi Liquid Singularities

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II. Interplay with Quantum Critical Behavior

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III. Experimental Indications of Mode-Mode Coupling Effects

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I. Fermi Liquid Singularities

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Fermi liquid phase described by stable RG fixed point ( Shankar )

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Leading scaling behavior usual FL properties

Example: Spin susceptibility

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Leading corrections to scaling? Provided by soft modes, e.g., p-h excitations

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Disordered systems: p-h excitations diffusive (scale dimension d-2)

Weak-localization type nonanalytic corrections

Example:

Derived in perturbation theory long before RG treatment
( Altshuler & Aronov )

Weak-localization effects not usually thought of as corrections to scaling, but they emerge from standard scaling arguments in the vicinity of a (disordered) FL fixed point ( TRK & DB )

Analogous singularities in other observables, and in T-dependences

Appears via integral over diffusive modes:

Clean systems: p-h excitations ballistic (scale dimension d-1)

Clean analogies to weak-localization corrections

Example: d=3:

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Leading corrections to scaling near clean FL fixed point

Early attempts (Landau theory, perturbation theory) led to confusion

Lately firmly established by perturbation theory

( DB, TRK & TV; Chitov & Millis; Chubukov & Maslov )

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Soft modes, resulting nonanalyticities occur in an entire phase

These are generic soft modes

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How big a deal? (After all, these are just standard corrections to scaling!)

Important consequences for QPTs !

II. Interplay with Quantum Critical Behavior

Critical fixed point Phase transition driven by critical soft modes
(OP fluctuations)

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Coupling between generic soft modes and OP fluctuations

Generic soft modes influence critical behavior, and vice versa

Simple LGW theory inadequate, coupled field theory is needed

Breakdown of Hertz's LGW program

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This can happen at classical transitions, too (e.g., compressible magnets), but

T=0 more soft modes more relevant for QPTs

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Examples: Various magnetic QPTs in metals

FM QPT ( TRK, DB, TV, et al ; Pepin et al )

AFM QPT ( Abanov & Chubukov ; Pepin et al )

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III. Experimental Indications of Mode-Mode Coupling Effects

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MnSi has interesting phase diagram and unusual behavior in the PM phase
( Pfleiderer, Julian & Lonzarich )

1st order transition, tricritical point, critical end point


2nd order in other materials (e.g., ZrZn₂) with mean-field exponents

T^3/2 dependence of the resisitivity in a whole region in the PM phase



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URuReSi is a disordered counterpart
Strongly non-mean field exponents

Also shows resistivity Tⁿ with n ~ 1.5 in the PM phase ( Bauer et al )

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Theory (the theory meister just can't resist):

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Clean case:

1st order transition: Fluctuation-induced

2nd order transition: Feedback effects suppress fluctuations that lead to 1st order transition Non-mean field 2nd order transition

Upper critical dimension d_c⁺ = 3 ( not 1 as in Hertz theory). This explains observation of mean-field exponents even though Hertz theory breaks down.

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Disordered case:

Transition always 2nd order

Strongly non-mean field, in agreement with experiment

Critical behavior in d=3 known exactly: Long-ranged fluctuations
Gaussian critical fixed point (almost, various DIVs)

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T^3/2 behavior of resistivity: Open question

Origin?

Breakdown of FL, or corrections to scaling?

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