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arXiv:2406.12729 · Physical review. B./Physical review. B

Spin-Peierls instability of deconfined quantum critical points

David Hofmeier, Josef Willsher, Urban F. P. Seifert, Johannes Knolle

Published Sep 13, 2024• 3 citations
arXivHTMLPDF

Abstract

Deconfined quantum critical points (DQCPs) are putative phase transitions beyond the Landau paradigm with emergent fractionalized degrees of freedom. The original example of a DQCP is the spin-$\frac{1}{2}$ quantum antiferromagnet on the square lattice which features a second-order transition between valence bond solid (VBS) and N\'eel order. The VBS order breaks a lattice symmetry, and the corresponding VBS order parameter may couple to lattice distortion modes (phonons) at appropriate momenta. We investigate a field-theoretic description of the DQCP in the presence of such a spin-lattice coupling. We show that treating phonons as classical lattice distortions leads to a relevant monopole-phonon interaction inducing an instability towards a distorted lattice by an analogous mechanism to the spin-Peierls instability in one dimension. Consequently, there is a breakdown of the DQCP which generally becomes a strong first-order transition. Taking into account the full quantum nature of the phonons, we argue that the continuous DQCP persists above a critical phonon frequency. Lastly, we comment on the connection to general gapless, deconfined gauge theories.

DOI
10.1103/physrevb.110.125130

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Deconfined quantum critical points (DQCPs) are putative phase transitions beyond the Landau paradigm with emergent fractionalized degrees of freedom. The original example of a DQCP is the spin-12\frac{1}{2}21​ quantum antiferromagnet on the square lattice which features a second-order transition between valence bond solid (VBS) and N'eel order. The VBS order breaks a lattice symmetry, and the corresponding VBS order parameter may couple to lattice distortion modes (phonons) at appropriate momenta. We investigate a field-theoretic description of the DQCP in the presence of such a spin-lattice coupling. We show that treating phonons as classical lattice distortions leads to a relevant monopole-phonon interaction inducing an instability towards a distorted lattice by an analogous mechanism to the spin-Peierls instability in one dimension. Consequently, there is a breakdown of the DQCP which generally becomes a strong first-order transition. Taking into account the full quantum nature of the phonons, we argue that the continuous DQCP persists above a critical phonon frequency. Lastly, we comment on the connection to general gapless, deconfined gauge theories.
Deconfined quantum critical points (DQCPs) describe continuous transitions between ordered phases beyond the Landau paradigm. A simple example is the Néel antiferromagnet (AFM) to valence bond solid (VBS) transition in a 1D antiferromagnetic J1−J2J_1-J_2J1​−J2​ model. In analogy to the spin-Peierls instability of critical spin chains, DQCPs are predicted to be unstable towards lattice distortions below a critical phonon frequency. In this work, we use tensor network simulations to investigate this instability in the antiferromagnetic J1−J2J_1-J_2J1​−J2​ model coupled to lattice vibrations. We confirm the stability of DQCP for large phonon frequencies and demonstrate that the transition turns strongly first-order below a critical frequency. The instability is caused by a reduction of the Luttinger parameter due to spin-phonon interactions and we identify the effective theory of the behavior as the double sine-Gordon model. The same effective theory is known to describe the classical Ashkin-Teller model, which enables us to show that the critical endpoint is in the four-state Potts universality class. We argue based on non-linear bosonization that the sign of the double-frequency term is fixed, which provides a microscopic justification for the first-order transition. Furthermore, we provide quantitative numerical scaling results for the phonon spectral function, offering an experimental signature to probe DQCP-phonon coupling in low-dimensional materials.
Abstract Deconfined quantum critical points (DQCPs) have been proposed as a class of continuous quantum phase transitions occurring between two ordered phases with distinct symmetry-breaking patterns, beyond the conventional framework of Landau-Ginzburg-Wilson (LGW) theory. At the DQCP, the system exhibits emergent gauge fields, fractionalized excitations, and enhanced symmetries. Here we review recent theoretical and experimental progress on exploring DQCPs in condensed matter systems. We first introduce theoretical advancements in the study of DQCPs over the past twenty years, particularly in magnetic models on square lattices, honeycomb lattices, kagome lattices, and one-dimensional spin chains. We then discuss recent progress on experimental realization of DQCP in quantum magnetic systems. Experimentally, the Shastry-Sutherland model, realized in SrCu2(BO3)2, offers a particularly promising platform for realizing DQCPs. The magnetic frustration inherent to this model drives phase transitions between two distinct symmetry-breaking states: a valence bond solid (VBS) phase and a Néel antiferromagnetic phase. Remarkably, SrCu2(BO3)2 has provided the first experimental evidence of a proximate DQCP through a field-induced Bose-Einstein condensation, transitioning from the VBS state to the Néel state. Nevertheless, the direct experimental realization of a DQCP remains a significant challenge. Despite this, it offers a promising platform for exploring emergent phenomena through quantum phase transition in low-dimensional quantum systems.
Deconfined quantum critical points (DQCPs) involving lattice symmetries evade the conventional Landau paradigm because the competing orders break incompatible internal and crystalline symmetries. We show that a class of DQCPs can nevertheless be understood as Landau-type transitions after gauging anomalous onsite symmetries. For spin chains with Lieb-Schultz-Mattis (LSM) anomalies, gauging produces a noninvertible lattice translation whose fusion closes only up to ordinary translations, giving rise to a crystalline categorical symmetry. In the gauged description, the original DQCP becomes a transition between different symmetry breaking patterns of this categorical symmetry. We demonstrate this mechanism in microscopic lattice models; the magnetic-valence-bond-solid (VBS) DQCP realizes a Rep(D8D_8D8​)-type crystalline categorical Landau transition, whereas a y-antiferromagnetic-VBS DQCP realizes a Rep(H8H_8H8​)-type one. Although Rep(D8D_8D8​) and Rep(H8H_8H8​) share the same fusion rules, they have inequivalent FFF-symbols and therefore define distinct categorical descriptions. Our results show that the universal categorical structure underlying these DQCPs is encoded in the full fusion category, rather than in the fusion ring alone.
The deconfined quantum critical point (DQCP) between the N\'eel and valence bond solid order was originally proposed in quantum spin systems with a local Hamiltonian. In the last few years analogs of DQCPs with nonlocal interactions have been explored, which can lead to rich possibilities. The nonlocal interactions can either arise from an instantaneous long-range interaction in the Hamiltonian, or from gapless modes that reside in one higher spatial dimension. Here, we consider another mechanism of generating nonlocal interactions by coupling the DQCP to the ``hot spots'' of a Fermi surface. We demonstrate that at least within a substantial energy window, the physics of the DQCP is controlled by a new fixed point with a dynamical exponent z>1z>1z>1.
Deconfined quantum critical points (DQCPs) are proposed as unconventional second-order phase transitions beyond the Landau-Ginzburg-Wilson paradigm. The nature and experimental realizations of DQCPs are crucial issues of importance. We illustrate the potential for DQCPs between the valence bond solid state and the antiferromagnetic phase to arise in optical lattices containing frustrated dipolar bosons subject to hard-core constraints. The emergence of DQCPs is comprehended through the fusion of two Berezinskii-Kosterlitz-Thouless (BKT) transitions. The DQCPs and the BKTs are confirmed by the scaling of ground-state fidelity susceptibilities in finite systems and the analysis of order parameters obtained from infinite systems. The numerical analysis reveals varying critical exponents of the correlation length in DQCPs and the logarithmic scaling in BKTs, respectively. In this paper, we offer a promising platform for realizing DQCPs and provide valuable insights into their nature within the framework of topological phase transitions.
The deconfined quantum critical point (DQCP) -- the enigmatic incarnation of the quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm of symmetries and their spontaneous breaking -- has been proposed and actively pursued for more than two decades. Various 2D quantum many-body lattice models, both in spin/boson and fermion representations have been tested with the state-of-the-art numerical techniques and field-theoretical analyses, and yet, the conclusion is still controversial. Experimental realizations of DQCP in the quantum magnet SrCu2_22​(BO3_33​)2_22​ and superconducting quantum criticality in 2D material have either shown first order transition or intermediate phase. The tension between the lattice scale details and the requirement from continuum limit, manifested in the form of the inconsistent critical scaling behavior and violations of generic conformal bootstrap bound, has not been resolved. Here we solve these decades-long controversies from the new and fundamental perspective of the quantum entanglement. We develop the incremental algorithm to compute the entanglement entropy at a fermionic DQCP with unprecedentedly accurate data and reveal the universal coefficient of the logarithmic correction therein is negative and at odds with positivity requirement of the conformal field theory. Together with results in other 2D DQCP lattice models (both in fermion and spin systems), our discoveries clearly demonstrate the 2D SU(2) antiferromagnet to valence bond solid DQCPs are not conformal fixed point and naturally explain the experimental difficulties in finding them. This marks the end of the beginning of unambiguous finding of the quantum phase transitions truely beyond the Landau-Ginzburg-Wilson paradigm, since its suggestion two decades ago.