Quantum phase transitions in holographic models of magnetism and superconductors

TL;DR

The paper constructs a holographic model of antiferromagnetism by condensing a neutral order parameter in a finite-density AdS background, capturing the SU(2) → U(1) symmetry-breaking pattern and its spin-wave excitations. By tuning the UV dimension of the order parameter across a critical value, it reveals a Berezinskii-Kosterlitz-Thouless type quantum phase transition governed by an emergent AdS$_2$ IR fixed point, with rich backreaction and zero-temperature IR structure. Embedding the neutral order parameter into an SU(2) triplet, the authors derive two gapless spin waves and establish their spin-wave velocity from holographic correlators, linking bulk Higgs physics to boundary Goldstone dynamics. They also analyze external magnetic field effects, finding a forced ferromagnetic magnon with quadratic dispersion and discuss broader implications for competing orders and fermionic probes in holographic quantum matter.

Abstract

We study a holographic model realizing an "antiferromagnetic" phase in which a global SU(2) symmetry representing spin is broken down to a U(1) by the presence of a finite electric charge density. This involves the condensation of a neutral scalar field in a charged AdS black hole. We observe that the phase transition for both neutral and charged (as in the standard holographic superconductor) order parameters can be driven to zero temperature by a tuning of the UV conformal dimension of the order parameter, resulting in a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type. We also characterize the antiferromagnetic phase and an externally forced ferromagnetic phase by showing that they contain the expected spin waves with linear and quadratic dispersions respectively.

Figures (11)

• Figure 1: A cartoon picture for the flow of the system induced by the condensation of a neutral scalar field. The CFT$_A$ refers to the $(0+1)$-dimensional IR CFT of the uncondensed system, described geometrically by an AdS$_2$ factor with radius $R_2$. When the dimension ${{\Delta}}$ of the operator is close to the quantum critical value ${{\Delta}}_c$, the system stays near this IR CFT for an exponentially long scale, before flowing to the new fixed point, $(0+1)$ CFT$_B$, described by an AdS$_2$ factor with a different radius $\tilde{R}_2$.
• Figure 2: Tuning the UV dimension of the order parameter we find quantum phase transitions between a (0+1) dimensional IR CFT corresponding to AdS$_2$ in the unbroken phase and various types of symmetry-breaking phases. The type of symmetry-broken phase depends on the charge $q$ of the order parameter.
• Figure 3: The constants $A$ and $B$ determine the behavior of the scalar profile asymptotically. This is a representative plot where we scan the case $m^2 R^2=-2.1$ and $T=0.00024$ (with $T/T_c=0.22$) by varying $\chi_h$. There is symmetry breaking if $A=0$$B\neq0$ in the normal quantization or if $A\neq0$$B=0$ in the alternative quantization.
• Figure 4: Phase diagram for the standard quantization. Note logarithmic scale for $T$. $C$ denotes the condensed phase and $U$ the uncondensed phase. $T_c \to 0$ as $m^2 \to m_c^2$, leading to a quantum critical point.
• Figure 5: Top: Plot for exponent $\beta$, defined as $B \sim (T_c-T)^{\beta}$. $\beta=0.49 \pm 0.03$ from numerical fit, compared with $\beta_{\mathrm{mean\;field}} = \frac{1}{2}$. Bottom: Plot for exponent $\delta$, defined as $B \sim A^{\frac{1}{\delta}}$ at $T_c$. $\delta=3.03 \pm 0.05$ from numerical fit, compared with $\delta_{\mathrm{mean\;field}} = 3$.