Quantum fluctuations of a nearly critical Heisenberg spin glass
By A. Georges, Olivier Parcollet, S. Sachdev. 2000
212 citations recorded by the source corpus.
We describe the interplay of quantum and thermal fluctuations in the infinite-range Heisenberg spin glass. This model is generalized to SU(N) symmetry, and we describe the phase diagram as a function of the spin S and the temperature T. The model is solved in the large N limit and certain universal critical properties are shown to hold to all orders in 1/N. For large S, the ground state is a spin glass, but quantum effects are crucial in determining the low T thermodynamics: we find a specific heat linear in T and a local spectral density of spin excitations linear in frequency for a spin glass state which is marginally stable to fluctuations in the replicon modes. For small S, the spin-glass order is fragile, and a spin-liquid state dominates the properties over a significant range of temperatures and frequencies. We argue that the latter state may be relevant in understanding the properties of strongly-disordered transition metal and rare earth compounds.
Subfields: Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/7909ff24784d2740281e3f6541db27a1cfbf3614
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In Condensed Matter Physics
Citations in the corpus
- Holographic Quantum Matter (2016, methodology): “Furthermore, it can be shown that not just the saddle-point equations, but also the entire action functional for the bilocal Green’s function [281; 424; 625; 642] is invariant under (608) at low energies.”
- Notes on the complex Sachdev-Ye-Kitaev model (2019, methodology): “Another key feature of the SYK models is the presence of a non-zero entropy in the zero temperature limit [4]: lim β→∞ lim N→∞ S(N,NQ, β−1) N = S(Q) > 0 , (1.”
- Translationally Invariant Non-Fermi-Liquid Metals with Critical Fermi Surfaces: Solvable Models (2018, background): “[49] for the q 1⁄4 4 case and for general q in Ref.”
- Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models (2016, methodology): “After introducing a pair of auxiliary bi-local fields “Green’s function” G(τ1, τ2) and “self-energy” Σ(τ1, τ2) and carrying out the disorder average of the partition function, the fermions can be integrated out, leaving [4, 38]:”
- Numerical study of fermion and boson models with infinite-range random interactions (2016, background): “The exact numerics shows a finite entropy density in the limit of vanishing temperature, with a value consistent with earlier analytic results [4][10].”
- What Can Gauge-Gravity Duality Teach Us about Condensed Matter Physics? (2011, background): “Such states now have a non-zero ground state entropy density [59, 61], a consequence of adding up the entropy of the finite density of decoupled quantum”
- Black holes and random matrices (2016, background): “Another possibility is that the very bottom of the spectrum would be controlled by a spin-glass phase that was argued to exist in the Sachdev-Ye model [48], and may also be present at exponentially low temperatures in the SYK model [62].”
- The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual (2017, methodology): “For the q = 4 SYK model, the transition to a glassy phase is expected at extremely low temperature, Tglass ∼ Je− √ N [5], so one may assume that T Tglass for almost all purposes.”
- Remarks on the Sachdev-Ye-Kitaev model (2016, methodology): “We assume that the system does not have a spin glass transition [31] and we work to leading order in the 1/N expansion.”
- Bekenstein-Hawking Entropy and Strange Metals (2015, background): “later extended [7, 8] to the fermion model of SY, in which we define S and Q per site, and there are no explicit CFT2 degrees freedom; instead each fermion site is influenced by a self-consistent environment, and this environment plays a role similar to that of the CFT2 in the Kondo problem.”