Dimensionality-Changing Transition from a Non-Fermi Liquid to a Spin-Solid in a Multichannel Kondo Lattice

Abstract

A multichannel Kondo system, where a single quantum spin couples to multiple channels of an electronic bath, provides one of the simplest examples of a zero-dimensional non-Fermi liquid. It is natural to ask: what happens when an extensive number of such systems are coupled together? A simple renormalization group argument implies that in a chain of SU(N) multichannel quantum systems, where each spin is coupled to its own bath of K channels, the individual spins dynamically decouple at low energy when N>K, resulting in a 'sliding' non-Fermi liquid. Using Quantum Monte Carlo (QMC) simulations, we find evidences of a continuous, 'dimensionality-changing' phase transition out of this non-Fermi liquid into a valence-bond solid phase as the intersite coupling is increased. Remarkably, at the critical point, correlations exhibit a power-law behavior even along the direction in which the spins are coupled, indicating the breakdown of dynamical decoupling at the transition. We also develop an RG scheme to understand the universal aspects of this transition.

Figures (12)

• Figure 1: (a) Geometry of the setup considered in this work: local moments carry an SU($N$) spin and form a 1d lattice, with each local moment coupled to separate $K$ channels of conduction electrons. (b) Phase diagram for $N = 4, K = 2$ based on sign-problem-free QMC simulations: as $J_H/J_K$ increases, one undergoes a phase transition from a phase where different local moments dynamically decouple and therefore the low-energy theory is a collection of decoupled 0+1-D non-Fermi liquids, to a phase where they strongly couple and form a valence-bond solid.
• Figure 2: VBS correlation ratio $R_{\textrm{VBS}}$ for $N=4$, $K=2$ as a function of $J_H/J_K$ for $J_K=W=1$. Insets show the real space dependence of the dimer-dimer correlation function $(-1)^xD(x)$ at $J_H/J_K=0.4$ (decoupled phase), $J_H/J_K=0.55$ (DCPT), and $J_H/J_K=0.8$ (VBS phase). At the DCPT, one observes a power-law decay of $(-1)^xD(x)$ with an exponent of 2.3.
• Figure 3: Space and time spin-spin correlation functions $S(x,\tau)$ at $N=4$ and $K=2$ for different $J_H/J_K$, corresponding to: (a,b) decoupled phase, (c,d) DCPT, and (e,f) VBS phase. For comparison, in panels (e) and (f), we also plot the data for the decoupled ($J_K=0$) SU(4) Heisenberg chain with a clear exponential decay of $S(x,\tau)$.
• Figure 4: Dynamical spin structure factor $S(q,\omega)$ in: (a) decoupled phase at $J_H/J_K=0.4$ and (b) VBS phase at $J_H/J_K=0.8$.
• Figure 5: Two characteristic fixed points of RG with one relevant direction. (a) When $\alpha = N C^2_{SSS} \gtrsim 8$, $|J_x|$ decays exponentially with oscillating sign structure. The figure shows the fixed point values of $J_x$ as a function of $x$ for $\alpha = 8, \epsilon = 1$ at a system size $L = 60$. The inset shows the 1-loop correction to the scaling dimension of the impurity, associated with the temporal spin-spin correlations, at the critical point for different system sizes. (b) When $\alpha = \mathcal{O}(1)$, one finds a different fixed point with a single relevant direction where $|J_x| \sim 1/L$ with an oscillating sign structure. The figure shows the solution for $\alpha = 4, \epsilon = 1$ at a system size $L = 60$. Both of these solutions are reachable by starting with short-range interactions where $J_{x=1}$ is the only non-zero coupling (as depicted by the dashed curve $J_{\textrm{initial}})$.