Session K07: Novel and Emerging Phases of Matter

Emergent Quantum Phase Transition of a Charge-Density-Wave Insulator

There are two broad classes of phase transitions known in critical phenomena: thermal phase transitions, which typically go from an ordered phase to a disordered phase (driven by thermal fluctuations) and quantum phase transitions, which typically go from an ordered phase to a quantum coherent phase at zero temperature (driven by quantum fluctuations). Here, we introduce a new class of transitions that lie in between these two, which we call an emergent quantum phase transition. This system has no quantum phase transition at T=0, but it has a transition (here a metal-to-insulator transition) that is present for all nonzero T including the limit as T approaches 0. At nonzero temperatures, the system displays similar behavior to that of a quantum-critical system, with scaling behavior seen in the resistivity, but the emergent quantum critical point does not arise from a thermal critical point being suppressed to T=0. We illustrate this phenomena with an exact solution of the emergent metal-insulator transition of the charge-density-wave phase in an electronic system that also has both thermal order-disorder transitions and a Mott-like metal-insulator transition. We discuss the origin of this phase through thermally activated defect states, and how one can identify this behavior in experimental systems. We also describe how it may also appear in spin-density-wave antiferomagnets in three dimensions.   

How prominent are microemulsion phases in 2D electron systems?

In two-dimensional electronic systems, direct first-order phase transitions are prohibited by the long-range Coulomb interaction, which implies a huge energy penalty for macroscopic phase separation. A prominent proposal is that direct first-order transitions are replaced by a series of "microemulsion" phases characterized by patterns of mesoscopic domains where the two phases are intermixed. In this work, we examine the range (Δn) of average electron density that these microemulsion phases may occupy. We demonstrate that, even without knowing the value of a phenomenological surface tension parameter, one can establish a robust upper bound for Δn. This result has wide-ranging implications for interpreting experiments. For the Wigner crystal - Fermi liquid transition, we derive a remarkably narrow bound, which helps to explain why microemulsion phases are not observed in quantum Monte Carlo studies.   

Anderson Critical Metal Phase in Trivial States Protected by C2zT Symmetry on Average

The joint symmetry C_2zT protects obstructed atomic insulators in 2D translational invariant magnetic materials, where electrons form molecule orbitals with charge centers away from the positions of atoms. The transitions from these states to atomic insulators have to go through an intermediate metallic phase accomplished by the emergence, evolution, and annihilation of Dirac points. We show that, under quenched weak chemical potential disorder that respects the C_2zT symmetry on average, the intermediate metallic phase remains delocalized (up to numerically accessible system sizes), where every point in a finite transition process is a scale-invariant critical metal in the thermodynamic limit. We thus refer to the delocalized metallic phase as a crystalline-symmetry-associated critical metal phase. The underlying mechanism cannot be explained by conventional localization theories, such as weak anti-localization and topological phase transition in the ten-fold way classification. Through a quantitative mapping between lattice models and network models, we find that the critical metal phase is equivalent to a quantum percolation problem with random fluxes. The criticality can hence be understood through a semi-classical percolation theory.   

Quantum crystallization in a Sombrero Metal

Recent experiments on lightly-doped multilayer graphene, where the conduction band assumes a "Mexican Hat" shape in the presence of a strong perpendicular displacement field, motivated us to propose a model 2D Hamiltonian called the sombrero metal. This model consists of isotropic Coulomb interactions and a kinetic energy dispersion ε_k = -αk²+βk⁴+α²/4β (α,β > 0) that takes the shape of a sombrero. We study the process of quantum crystallization and the intermediate phases of the sombrero metal at zero-temperature using the Hartree-Fock approximation. We find that quantum crystallization occurs sequentially as we decrease the electron density or increase the interaction strength. Firstly, it develops local orientation by forming a nematic Fermi liquid; then, due to anisotropy in dispersion, it forms an electron liquid-crystal where translational order is broken only in one direction and eventually becomes a Wigner crystal where translational symmetry is fully broken. We find that in the electron liquid-crystal phase, the electron density exhibits a periodicity nearly half that of the unit cell to significantly lower its Hartree energy. Our findings provide a foundational understanding of the crystallization process and phase transitions in the Sombrero Metal.   

Dynamics of Dipolar BECs

We consider layered Bose-Einstein condensates interacting via contact intra-condensate interactions and dipolar inter-condensate potentials, both of which dominate intercondensate

tunneling (which we neglect for simplicity). For this system, we find the normal modes, we study its localization properties by numerically computing the inverse participation ratio, and we compute the inter-tube shear viscosity.   

SU(2)xU(1) gauge theory for magnetic and pairing fluctuations in the 2D Hubbard model

We analyze the interplay of antiferromagnetism and pairing fluctuations in the two dimensional Hubbard model with a moderate repulsive interaction. In particular, we present a gauge theory description for fluctuations where the stiffnesses are computed in the coexisting phase from renormalization mean-field equations via the functional renormalization group (fRG). We show a sizable doping regime with robust pairing coexisting with Néel or incommensurate antiferromagnetism. The fluctuations suppress any magnetic order at finite temperature while the Kosterlitz-Thouless critical temperature for pairing remains finite.   

Solvabel model for 2+1D quantum critical points: Loop soups of 1+1D conforaml field theories

We construct a class of solvable models for 2+1D quantum critical points by attaching 1+1D conformal field theories (CFTs) to fluctuating domain walls forming a "loop soup". Specifically, our local Hamiltonian attaches gapless spin chains to the domain walls of a triangular lattice Ising antiferromagnet. The macroscopic degeneracy between antiferromagnetic configurations is split by the Casimir energy of each decorating CFT, which is usually negative and thus favors a short loop phase with a finite gap. However, we found a set of 1D CFT Hamiltonians for which the Casimir energy is effectively positive, making it favorable for domain walls to coalesce into a single "snake" which is macroscopically long and thus hosts a CFT with a vanishing gap. The snake configurations are geometrical objects also known as fully-packed self-avoiding walks or Hamiltonian walks which are described by an O(n=0) loop ensemble with a non-unitary 2+0D CFT description. Combining this description with the 1+1D decoration CFT, we obtain a 2+1D theory with unusual critical exponents and entanglement properties. Regarding the latter, we show that the log contributions from the decoration CFTs conspire with the spatial distribution of loops crossing the entanglement cut to generate a "non-local area law". Our predictions are verified by Monte Carlo simulations.   

Conformal invariance and multifractality at Anderson transitions in arbitrary dimensions

Multifractals arise in various systems across nature whose scaling behavior is characterized by a continuous spectrum of multifractal exponents Δ_q. In the context of Anderson transitions, the multifractality of  critical wavefunctions is described by operators O_q with scaling dimensions Δ_q in a field theory description of the transitions. The operators O_q satisfy the so-called Abelian fusion, expressed as a simple operator product expansion. Assuming conformal invariance and Abelian fusion, we use the conformal bootstrap framework to derive a constraint that implies that the multifractal spectrum Δ_q (and its generalized form) must be quadratic in its arguments in any dimension d ≥ 2.   

Quantum Hall Phases from Dipolar Symmetry Breaking

The spontaneous breaking of multipole symmetries has been a matter of recent interest, leading to novel phases of matter such as Bose condensates without a Meissner effect and Fermi surfaces without quasiparticles [1,2]. Here, we investigate the related question of fermionic dipole symmetry-breaking orders that exhibit nontrivial topology. We compute the mean-field phase diagram of a 2-d dipole-symmetric model where the symmetry-breaking ground states are band insulators with a variable Chern number. The Chern number of the occupied band is found to determine both the counting and dispersion of the Goldstone modes of the broken dipole symmetry. At the topological phase transition from a trivial insulator to a Chern insulator, we study a novel quantum critical point featuring an emergent Dirac fermion coupled to the dipolar Goldstone modes. We additionally discuss the boundary theory of the mean-field ground states, and show that the boundary mode remains chiral but acquires a cubic dispersion. 

[1] Ethan Lake, Michael Hermele, and T. Senthil. Dipolar bose-hubbard model. Phys. Rev. B, 106:064511, Aug 2022.

[2] Amogh Anakru and Zhen Bi. Non-fermi liquids from dipolar symmetry breaking. Phys. Rev. B, 108:165112, Oct 2023.   

Dipolar quantum solids emerging in a Hubbard quantum simulator

Long-range interactions play an important role in nature; however, quantum simulations of lattice systems have largely not been able to realize such interactions. A wide range of efforts are underway to explore long-range interacting lattice systems using AMO and condensed matter platforms. We achieve novel quantum phases in a strongly correlated lattice system with long-range dipolar interactions using ultracold magnetic erbium atoms. As we tune the dipolar interaction to be the dominant energy scale in our system, we observe quantum phase transitions from a superfluid into dipolar quantum solids, which we directly detect using site-resolved quantum gas microscopy. Furthermore, we study quantum phase transitions in the context of $Z_2$ lattice gauge theory by mapping the hard-core Bose-Hubbard model to the mixed-dimensional spin model. In addition, we share progress toward studying extended Fermi-Hubbard physics with the fermionic isotope of erbium. This work demonstrates that novel strongly correlated quantum phases can be studied using dipolar interaction in optical lattices, opening the door to quantum simulations of a wide range of lattice models with long-range and anisotropic interactions.   

Charge-4e superconductivity from nematic superconductor: study based on a generalized XY model

Charge-4e superconductivity is an intriguing state of matter that has gained considerable attention in recent years. Previous studies have suggested that this exotic phase can arise from multicomponent superconductors such as the pair-density-wave or the nematic superconductor. In this work, we propose a concrete model on the honeycomb lattice with a nematic superconducting ground state. With Monte Carlo simulations, we reveal a complex and promising finite-temperature phase diagram which not only includes the charge-4e phase but also a new phase exhibiting both nematic and charge-4e quasi-long-range orders. Furthermore, we demonstrate that the proliferation of domain walls, in addition to the vortices, also plays a significant role in the phase transitions involving charge-4e. Our findings offer valuable insights into the role of domain walls and the interplay between superconducting and nematic vortices in the charge-4e superconductivity phenomenon.   

Deconfined quantum criticality lost

Over the past two decades, the enigma of the deconfined quantum critical point (DQCP) attracted broad attention across condensed matter and quantum materials to quantum field theory and high-energy physics communities, as it is expected to offer a new paradigm in theory, experiment, and numerical simulations that goes beyond the Landau-Ginzburg-Wilson framework of symmetry breaking and phase transitions. However, the lattice realizations of DQCP have been controversial. For instance, in the square-lattice spin-1/2 J-Q model, believed to realize the DQCP between Néel and valence bond solid states, conflicting results, such as first-order versus continuous transition, and drifting critical exponents incompatible with conformal bootstrap bounds, have been reported. Here, we solve this two-decades-long mystery by taking a new viewpoint, in that we systematically study the entanglement entropy of square-lattice SU(N) DQCP spin models, from N=2,3,4 within the J-Q model to N=5,6,…,12,15,20 within the J1-J2 model. We unambiguously show that for N≤6, the previously determined DQCPs do not belong to unitary conformal fixed points. In contrast, when N≥Nc with a finite Nc≥7, the DQCPs correspond to unitary conformal fixed points that can be understood within the Abelian Higgs field theory with N complex components. From the viewpoint of quantum entanglement, our results suggest the realization of a genuine DQCP between Néel and valence bond solid phases at finite N, and yet explain why the SU(2) case is ultimately weakly-first-order, as a consequence of a collision and annihilation of the stable critical fixed point of the N-component Abelian Higgs field theory with another, bicritical, fixed point, in agreement with four-loop renormalization group calculations. The experimental relevance of our findings is discussed.   

Building boundary/interface conformal theory from SYK interactions

Coupling defects to extended critical degrees of freedom results in a class of intriguing theories known as the defect conformal field theory (CFT), which aids in our understanding of both quantum entanglement and holographic aspects of gravity. We construct such a theory by coupling the 1+1D CFT of N Majorana chains with an SYK-type interaction at a defect site. This gives rise to a family of boundary/interface CFTs between the SYK side of the chains to the rest. We compute the entanglement entropy between these two segments and found a logarithmic dependence on the system size. Notably, increasing the coupling strength leads to a continuous decrease of the coefficient to the logarithm, i.e., the central charge at the boundary. The result is buttressed by a saddle point analysis for large N values and a Gaussian fermionic state simulation for smaller N's. Our contributions highlight a novel defect conformal theory, extending the traditional concepts found in the Ising CFT.   

Generalized symmetries in ordered phases and applications to disordering

In this talk, we show that higher-form and non-invertible symmetries generally emerge in ordered phases and discuss their ability to predict and classify phase transitions into neighboring disordered phases. These transitions are driven by spontaneously breaking the emergent generalized symmetries. While the resulting phase is disordered, it is nontrivial, hosting (non-)abelian topological order, emergent gauge bosons, and fractionalized symmetry charges. We will highlight a few simple examples but focus on an isotropic antiferromagnet in 3D space. Using the emergent generalized symmetries (which include higher-form and non-invertible symmetries), we show that there exists a transition out of the antiferromagnetic phase to a paramagnetic phase that has emergent photons and a gapless mode that behaves like an emergent axion. These results demonstrate that even the most exotic generalized symmetries emerge in ordinary phases and provide a valuable framework for characterizing them and their transitions.   

Higher-form Symmetries under Weak Measurement

We aim to address the following question: if we start with a quantum state with a spontaneously broken higher-form symmetry, what is the fate of the system under weak local quantum measurements? We demonstrate that under certain conditions, a phase transition can be driven by weak measurements, which suppresses the spontaneous breaking of the 1-form symmetry and weakens the 1-form symmetry charge fluctuation. We analyze the nature of the transitions employing the tool of duality, and we demonstrate that some of the transitions driven by weak measurement enjoy a line of fixed points with self-duality.