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arXiv:2110.00007 · Physical review. B./Physical review. B

Spin liquid to spin glass crossover in the random quantum Heisenberg magnet

Maine Christos, Felix M. Haehl, Subir Sachdev A

Published Feb 14, 2022• 20 citations
arXivHTMLPDF

Abstract

We study quantum SU($M$) spins with all-to-all and random Heisenberg exchange interactions of root-mean-square strength $J$. The $M\ensuremath{\rightarrow}\ensuremath{\infty}$ model has a quantum spin liquid ground state with the spinons obeying the equations of the Sachdev-Ye-Kitaev (SYK) model. Numerical studies of the SU(2) model with $S=1/2$ spins show spin glass order in the ground state, but also display SYK spin liquid behavior in the intermediate frequency spin spectrum. We employ a $1/M$ expansion to describe the crossover from fractionalized fermionic spinons to a confining spin glass state with weak spin glass order ${q}_{EA}$. The SYK spin liquid behavior persists down to a frequency ${\ensuremath{\omega}}_{*}\ensuremath{\sim}J{q}_{EA}$, and for $\ensuremath{\omega}<{\ensuremath{\omega}}_{*}$, the spin spectral density is linear in $\ensuremath{\omega}$, thus quenching the extensive zero temperature entropy of the spin liquid. The linear $\ensuremath{\omega}$ spectrum is qualitatively similar to that obtained earlier using bosonic spinons for large ${q}_{EA}$. We argue that the extensive SYK spin liquid entropy is transformed as $T\ensuremath{\rightarrow}0$ to an extensive complexity of the spin glass state. We comment on holographic connections of the confinement transition to the fragmentation of black holes with ${\mathrm{AdS}}_{2}$ horizons.

DOI
10.1103/physrevb.105.085120

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We study quantum SU(MMM) spins with all-to-all and random Heisenberg exchange interactions of root-mean-square strength JJJ. The M\ensuremath→\ensuremath∞M\ensuremath{\rightarrow}\ensuremath{\infty}M\ensuremath→\ensuremath∞ model has a quantum spin liquid ground state with the spinons obeying the equations of the Sachdev-Ye-Kitaev (SYK) model. Numerical studies of the SU(2) model with S=1/2S=1/2S=1/2 spins show spin glass order in the ground state, but also display SYK spin liquid behavior in the intermediate frequency spin spectrum. We employ a 1/M1/M1/M expansion to describe the crossover from fractionalized fermionic spinons to a confining spin glass state with weak spin glass order qEA{q}_{EA}qEA​. The SYK spin liquid behavior persists down to a frequency \ensuremathω∗\ensuremath∼JqEA{\ensuremath{\omega}}_{*}\ensuremath{\sim}J{q}_{EA}\ensuremathω∗​\ensuremath∼JqEA​, and for \ensuremathω<\ensuremathω∗\ensuremath{\omega}<{\ensuremath{\omega}}_{*}\ensuremathω<\ensuremathω∗​, the spin spectral density is linear in \ensuremathω\ensuremath{\omega}\ensuremathω, thus quenching the extensive zero temperature entropy of the spin liquid. The linear \ensuremathω\ensuremath{\omega}\ensuremathω spectrum is qualitatively similar to that obtained earlier using bosonic spinons for large qEA{q}_{EA}qEA​. We argue that the extensive SYK spin liquid entropy is transformed as T\ensuremath→0T\ensuremath{\rightarrow}0T\ensuremath→0 to an extensive complexity of the spin glass state. We comment on holographic connections of the confinement transition to the fragmentation of black holes with AdS2{\mathrm{AdS}}_{2}AdS2​ horizons.
A central question in frustrated quantum magnets is how quantum fluctuations destabilize spin-glass order and promote quantum spin-liquid behavior. We study the equilibrium dynamics of an infinite-range quantum Heisenberg model with random couplings, in which local magnetic moments arise from N_{f} flavors of spinful fermions. We employ an expansion in N_{f}, which controls the strength of quantum fluctuations, and self-consistently include 1/N_{f} corrections to the Luttinger-Ward functional. In the large-N_{f} limit, where quantum fluctuations are weak, the high- and low-temperature phases are respectively paramagnetic and spin glass ordered, with a transition temperature independent of N_{f}. For small numbers of fermionic flavors, however, quantum fluctuations substantially suppress the ordering temperature. We show that this behavior reflects the proximity of the system to a Sachdev-Ye-Kitaev (SYK) regime, realizing quantum spin-liquid dynamics over a broad range of finite frequencies, where both fermionic and spin spectral densities display critical behavior over a broad range of finite frequencies, with the latter exhibiting the scale-invariant form χ^{''}(ω)∼sgn(ω). At the lowest energies and temperatures, spin glass dynamics ultimately take over, producing a universal sub-Ohmic dynamical spin susceptibility χ^{''}(ω)∼sgn(ω)sqrt[|ω|]. Our results highlight a direct connection between the suppression of spin-glass order and the emergence of SYK criticality in a frustrated quantum magnet.
"Strange metals" with resistivity depending linearly on temperature T down to low T have been a long-standing puzzle in condensed matter physics. Here, we consider a lattice model of itinerant spin-[Formula: see text] fermions interacting via onsite Hubbard interaction and random infinite-ranged spin-spin interaction. We show that the quantum critical point associated with the melting of the spin-glass phase by charge fluctuations displays non-Fermi liquid behavior, with local spin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. This extends the quantum spin liquid dynamics previously established in the large-M limit of [Formula: see text] symmetric models to models with physical [Formula: see text] spin-[Formula: see text] electrons. Remarkably, the quantum critical regime also features a Planckian linear-T resistivity associated with a T-linear scattering rate and a frequency dependence of the electronic self-energy consistent with the marginal Fermi liquid phenomenology.
Quantum spin liquids are long-range entangled states of matter with emergent gauge fields and fractionalized excitations. While candidate materials, such as the Kitaev honeycomb ruthenate $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, show magnetic order at low temperatures TTT, here we demonstrate numerically a dynamical crossover from magnonlike behavior at low TTT and frequencies $\ensuremath{\omega}$ to long-lived fractionalized fermionic quasiparticles at higher TTT and $\ensuremath{\omega}$. This crossover is akin to the presence of spinon continua in quasi-1D spin chains. It is further shown to go hand in hand with persistent typicality down to very low TTT. This aspect, which has also been observed in the spin-1/2 kagome Heisenberg antiferromagnet, is a signature of proximate spin liquidity and emergent gauge degrees of freedom more generally, and can be the basis for the numerical study of many finite-TTT properties of putative spin liquids.
A brief survey of some random quantum models with infinite-range couplings is presented, ranging from the quantum Ising model to the Sachdev-Ye-Kitaev model. The Sachdev-Ye-Kitaev model was the first to realize an extensive zero temperature entropy without requiring an exponentially large ground state degeneracy. This phenomenon is closely linked to the absence of a particle-like interpretation of its low energy spectrum--its spectral functions are not those of bosons or fermions but are instead "Planckian", meaning they are universal functions of energy/temperature. A remarkable consequence of these properties is that the SYK model provides an effective low energy theory of non-supersymmetric charged or rotating black holes in 3+1 dimensions, leading to new results on the density of many-body quantum states of such black holes. For applications to non-quasiparticle metallic states of quantum materials, an extension of the SYK model, known as the two-dimensional Yukawa-Sachdev-Ye-Kitaev model, is required. The 2dYSYK model describes quantum phase transitions in metals with spatial inhomogeneity in the position of the quantum critical point. This extension has led to a universal theory of the strange metal state observed in numerous correlated electron compounds, including copper-oxide based high temperature superconductors.
We explore the nature of the quantum phase transition between a magnetically ordered state with collinear spin pattern and a gapless Z2{Z}_{2}Z2​ spin liquid in the Heisenberg-Kitaev model. We construct a slave particle mean-field theory for the Heisenberg-Kitaev model in terms of complex fermionic spinons. It is shown that this theory, formulated in the appropriate basis, is capable of describing the Kitaev spin liquid as well as the transition between the gapless Z2{Z}_{2}Z2​ spin liquid and the so-called stripy antiferromagnet. Within our mean-field theory, we find a discontinuous transition from the Z2{Z}_{2}Z2​ spin liquid to the stripy antiferromagnet. We argue that subtle spinon confinement effects, associated with the instability of gapped U(1)U(1)U(1) spin liquid in two spatial dimensions, play an important role at this transition. The possibility of an exotic continuous transition is briefly addressed.
We study quantum disordered ground states of the two-dimensional Heisenberg-Kitaev model on the triangular lattice using a Schwinger boson approach. Our aim is to identify and characterize potential gapped quantum spin liquid phases that are stabilized by anisotropic Kitaev interactions. For antiferromagnetic Heisenberg and Kitaev couplings and sufficiently small spin SSS, we find three different symmetric Z2{Z}_{2}Z2​ spin liquid phases, separated by two continuous quantum phase transitions. Interestingly, the gap of elementary excitations remains finite throughout the transitions. The first spin liquid phase corresponds to the well-known zero-flux state in the Heisenberg limit, which is stable with respect to small Kitaev couplings and develops ${120}^{\ensuremath{\circ}}$ order in the semiclassical limit at large SSS. In the opposite Kitaev limit, we find a different spin liquid ground state, which is a quantum disordered version of a magnetically ordered state with antiferromagnetic chains, in accordance with results in the classical limit. Finally, at intermediate couplings, we find a spin liquid state with unusual spin correlations. Upon spinon condensation, this state develops Bragg peaks at incommensurate momenta in close analogy to the magnetically ordered Z2 vortex crystal phase, which has been analyzed in recent theoretical works.