A deconfined quantum phase transition (DQPT) provides an extraordinary possibility of the quantum phase transition beyond the Ginzburg-Landau paradigm, which is interwoven with numerous exotic phenomena of the strongly correlated quantum many-body system, e.g., fractional excitation, emergent symmetries, and gauge field. However, various candidates of DQPT have been demonstrated to be weakly first order, and the conformal field theory has to be altered into a nonunitary one. Here we numerically found two linear dispersions with different velocities in one of the few survivors of DQPT---the extended hard-core Bose-Hubbard model on the kagome lattice. Such counterintuitive results directly lead to the negation of possible emergent Lorentz symmetry and the breakdown of conventional theory of DQPT. Furthermore, the snapshots of boson configuration hint that these two velocities may correspond to the dynamics of the fractional excitations and quantum strings, respectively. Our work will inspire researchers to revisit the theory of DQPT and benefit the field of quantum materials and quantum simulations.
We investigate the deconfined quantum critical point (DQCP) candidate in the extended hard-core Bose-Hubbard model on the kagome lattice, employing quantum Monte Carlo simulations to study the entanglement entropy and the
U(1) disorder operator. In stark contrast to findings in
J-
Q models and other candidates, the universal logarithmic correction coefficients for both quantities are found to be {positive}, consistent with a unitary conformal field theory (CFT). Crucially, the current central charge
CJ, extracted from the small-angle behavior of the disorder operator, is enhanced by a factor of approximately {4/3} compared to that of the conventional 3D
O(2) Wilson-Fisher fixed point. This enhancement {implies} a consistent explanation in the recently observed low-energy excitation spectrum at this DQCP, which features {two distinct linearly dispersing modes} with a velocity ratio of approximately three. Our results provide evidence that this quantum phase transition constitutes a genuine DQCP, characterized by coexisting fractionalized excitations that collectively modify its critical properties.
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.
We use large scale quantum Monte Carlo simulations to study an extended Hubbard model of hard core bosons on the kagome lattice. In the limit of strong nearest-neighbor interactions at 1/3 filling, the interplay between frustration and quantum fluctuations leads to a valence bond solid ground state. The system undergoes a quantum phase transition to a superfluid phase as the interaction strength is decreased. It is still under debate whether the transition is weakly first order or represents an unconventional continuous phase transition. We present a theory in terms of an easy plane noncompact CP^{1} gauge theory describing the phase transition at 1/3 filling. Utilizing large scale quantum Monte Carlo simulations with parallel tempering in the canonical ensemble up to 15552 spins, we provide evidence that the phase transition is continuous at exactly 1/3 filling. A careful finite size scaling analysis reveals an unconventional scaling behavior hinting at deconfined quantum criticality.
We investigate the nature of quantum spin liquid (QSL) phase of the spin-
1/2 nearest-neighbor XXZ antiferromagnet on the kagome lattice. Recent numerical calculations suggest that such a kagome spin liquid is insensitive to the XXZ anisotropy and is adjacent to a chiral spin liquid phase. Reformulating the problem in terms of a
U(1) lattice gauge theory with dynamical bosonic spinons, we propose that the kagome spin liquid can be understood as a deconfined critical phase extended by the
U(1) gauge fluctuation from a deconfined critical point between a symmetry-protected topological phase and a superfluid phase. Crucially, the stability of this QSL is ensured by the gauge fluctuation and hence our description necessarily falls beyond the conventional mean-field constructions of QSLs. Our work also makes an interesting connection between the critical spin liquid, deconfined criticality, symmetry protected topological phase and topological order.
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 SrCu
2(BO
3)
2 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.
Using Quantum Monte Carlo simulations, we study a series of models of fermions coupled to quantum Ising spins on a square lattice with
N flavors of fermions per site for
N=1,2 and
3. The models have an extensive number of conserved quantities but are not integrable, and have rather rich phase diagrams consisting of several exotic phases and phase transitions that lie beyond Landau-Ginzburg paradigm. In particular, one of the prominent phase for
N>1 corresponds to
2N gapless Dirac fermions coupled to an emergent
Z2 gauge field in its deconfined phase. However, unlike a conventional
Z2 gauge theory, we do not impose the `Gauss's Law' by hand and instead, it emerges due to spontaneous symmetry breaking. Correspondingly, unlike a conventional
Z2 gauge theory in two spatial dimensions, our models have a finite temperature phase transition associated with the melting of the order parameter that dynamically imposes the Gauss's law constraint at zero temperature. By tuning a parameter, the deconfined phase undergoes a transition into a short range entangled phase, which corresponds to N\'eel/Superconductor for
N=2 and a Valence Bond Solid for
N=3. Furthermore, for
N=3, the Valence Bond Solid further undergoes a transition to a N\'eel phase consistent with the deconfined quantum critical phenomenon studied earlier in the context of quantum magnets.