Field-driven quantum phase transitions in $S=1/2$ spin chains

Abstract

We study the magnetization process of a 1D extended Heisenberg model, the $J$-$Q$ model, as a function of an external magnetic field. In this model, $J$ represents the traditional antiferromagnetic Heisenberg exchange and $Q$ is the strength of a competing four-spin interaction. Without external field, this system hosts a twofold-degenerate dimerized (valence-bond solid) state above a critical value $q_c\approx 0.85$ where $q\equiv Q/J$. The dimer order is destroyed and replaced by a partially polarized translationally invariant state at a critical field value. We find magnetization jumps (metamagnetism) between the partially polarized and fully polarized state for $q>q_{\min }$, where we have calculated $q_{\min }=2/9$ exactly. For $q>q_{\min }$ two magnons (flipped spins on a fully polarized background) attract and form a bound state. Quantum Monte Carlo studies confirm that the bound state corresponds to the first step of an instability leading to a finite magnetization jump for $q>q_{\min }$. Our results show that neither geometric frustration nor spin-anisotropy are necessary conditions for metamagnetism. Working in the two-magnon subspace, we also find evidence pointing to the existence of metamagnetism in the unfrustrated $J_1$-$J_2$ chain ($J_1>0$, $J_2<0$), but only if $J_2$ is spin-anisotropic. We also investigate quantum-critical scaling near the transition into the fully polarized state for $q\le q_{\min }$ at $T>0$. While the expected `zero-scale-factor' universality is clearly seen for $q=0$ and $q\ll q_{\min }$; closer to $q_{\min }$ we find that extremely low temperatures are required to observe the asymptotic behavior, due to the influence of the tricritical point at $q_{\min }$, which leads to a cross-over at a temperature $T^{\ast }(q)$ between logarithmic tricritical scaling and zero-scale-factor universality, with $T^{\ast }(q)\to 0$ when $q\to q_{\min }$.

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Cited by in corpus (10)

• Random-Singlet Phase in Disordered Two-Dimensional Quantum Magnets
• Quantum criticality of spinons
• Quantum-critical scaling properties of the two-dimensional random-singlet state
• Metamagnetism and zero-scale-factor universality in the two-dimensional $J$-$Q$ model
• Pair hopping in systems of strongly interacting hard-core bosons
• Magnetization jump in one dimensional $J-Q_2$ model with anisotropic exchange
• Bose-Einstein condensation of deconfined spinons in two dimensions
• Magnetic effects of non-magnetic impurities in gapped short-range resonating valence bond spin liquids
• Improvements to the Stochastic Series Expansion method for the $J{Q}_2$ model with a magnetic field
• Field-induced freezing in the unfrustrated Ising antiferromagnet