Session W08: Quantum Phase Transition and Critical Matter

Interacting Fractons in 2+1D Quantum Field Theory

We analyze, in perturbation theory, a theory of weakly interacting fractons and non-relativistic fermions in a 2+1 dimensional Quantum Field Theory. In particular we compute the 1-loop corrections to the self energies and interaction vertex, and calculate the associated 1-loop Renormalization Group flows of the coupling constants. Surprisingly, we find that the fracton-fermion coupling does not flow due to an emergent coordinate-dependent symmetry of the effective Lagrangian, making this model a well-defined quantum field theory. We provide additional discussions on the regularization and renormalization of interacting fractonic theories, as well as both qualitative and quantitative remarks regarding the theory at finite temperature and finite chemical potential.   

Coulomb-Induced Nematicity in a Two-Valley Two-Dimensional Electron Gas

Recent experiments conducted in AlAs have revealed a transition as a function of decreasing electron density from a C₄ symmetric liquid to a nematic liquid phase, devoid of spin-ordering.  In a separate variational Monte Carlo study [1] of an appropriate two-valley model of the two-dimensional electron gas (2DEG), we showed that for effective mass anisotropy characteristic of AlAs, such a nematic phase arises as a form of valley polarization driven purely by the Coulomb repulsion between electrons.   To obtain greater insight into the essential physics, we have studied this same problem by expanding about the high density (small r_s) limit.  At Hartree-Fock level, a Stoner instability to a polarized state occurs below an unrealistically small critical value of r_s, and spin and orbital polarization are degenerate instabilities.  Extending the analysis of correlation energy within the random-phase approximation, we find an increase in the critical value of r_s, and prove that the nematic state consistently possesses a lower correlation energy compared to the non-nematic ferromagnetic state.  This observation is valid for more general repulsive interaction. We have also studied [2] the dilute limit (large r_s) and found that the system forms a nearly triangular Wigner crystal (WC) albeit one that is also nematic in the sense that it breaks the six-fold rotational symmetry of the single component WC. This outcome can be attributed to the phonons of the Wigner crystal inheriting the inherent "nematicity" of the kinetic energy.

[1] A. Valenti, V. Calvera, S. A. Kivelson, E. Berg, and S. D.Huber, arXiv:2307.15119 (2023)

[2] V. Calvera, S. Kivelson, E. Berg, Fiz. Nyzk. Temp., 49, 747-769 (2023)   

Constraining bosonized EFT of fermi liquids using lorentz and conformal invariance

Conformal field theories at finite chemical potential exhibit a rich phase structure under RG flow. One of the possible low energy 

phases is a fermi liquid. In this work we use a bosonised effective field theory (EFT) of fermi liquid to study the implications of spontaneously

broken lorentz and conformal invariance on the low energy wilson coefficients of our EFT. We test our non-linear constraints in weakly coupled

microscopic models of fermi liquids. We comment on the possibility of imposing further constraints on the landau parameters from causality

and unitarity of the UV CFT.    

Thermal conductivity near the quantum critical point in TmVO4

Thulium vanadate (TmVO₄) is a model system for exploring electronic nematicity, undergoing a continuous ferroquadrupolar (nematic) phase transition at 2.15 K that can be tuned with magnetic field to a T = 0 quantum critical point. The quadrupolar moments of local Tm-ion 4f orbitals are strongly coupled to lattice strain, with a cooperative Jahn-Teller distortion from tetragonal to orthorhombic at the transition. Although the transition at low field can be well described by a mean-field semiclassical treatment of the transverse-field Ising model, clear deviations have been observed upon approaching the quantum critical point [1].

As a probe sensitive to lattice dynamics as seen via phonon transport, thermal conductivity is well suited for investigating this physics. Here we present our measurements of the thermal conductivity of TmVO₄ as a function of magnetic field at dilution fridge temperatures, focusing particularly on the phase boundary in the vicinity of the quantum critical point.

[1] P. Massat et al., PNAS 119, e2119942119 (2022).   

Quantum Monte Carlo calculation of critical exponents of the Gross-Neveu-Yukawa on a two-dimensional fermion lattice model

It is expected that the Gross-Neveu-Yukawa (GNY) chiral Ising transition of Dirac fermions coupled with a scalar field in (2+1) dimensions will be the first fermionic quantum critical point that various methods, such as conformal bootstrap, perturbative renormalization group, and quantum Monte Carlo (QMC) simulations, would yield converged critical exponents—serving the same role as the Ising and O(N) models in the textbooks of statistical and quantum physics. However, such an expectation has not been fully realized from the lattice QMC simulations due to the obstacles introduced by the UV finite-size effect. In this Letter, by means of the elective-momentum ultrasize (EMUS)-QMC method, we compute the critical exponents of the O(N/2)2⋊Z2 GNY N=8 chiral Ising transition on a two-dimensional π-flux fermion lattice model between Dirac semimetal and quantum spin Hall insulator phases. With the matching of fermionic and bosonic momentum transfer and collective update in momentum space, our QMC results provide fully consistent exponents with those obtained from the bootstrap and perturbative approaches. In this way, the EMUS now live happily on the N=8 island and could explore the chiral Gross-Neveu-Yukawa archipelago with ease.   

Multicritical point and unified description of broken-symmetry phases in spin-12 antiferromagnets on a square lattice

We show that several distinct broken-symmetry phases in a spin-12 antiferromagnet on a square lattice with easy-plane anisotropy, including valence bond solid, chiral spin liquid, and the XY-ordered state, can all be accessed by perturbing a multicritical point with two massless Dirac fermions coupled to a level-one Chern-Simons gauge field. This allows for a unified description of these phases, as well as the phase transitions between them. In a specific phase transition, our analysis provides a lattice realization of one of the recently proposed fermion-boson dualities, thus lending support to it. We also briefly discu   

Suppression of the spin density wave in Sr3Ru2O7 with hydrostatic pressure

Measuring the resistivity of high purity single crystals of Sr₃Ru₂O₇ under pressure, we find strong evidence that the field-induced spin density wave phase at the metamagnetic transition is suppressed at a surprisingly low pressure of ∼ 3 ± 1 kbar. This offers the possibility of studying a bare quasi-two-dimensional spin-density-wave quantum critical point.   

Ferromagnet to spin glass transition in 2d Ising models

With random bonds of both signs, the classical two-dimensional Ising model undergoes a ferromagnet-to-paramagnet transition at low temperatures which is still little understood. The transition is governed by a zero-temperature fixed point separating ferromagnetic and spin-glass ground states. We use efficient evaluation of ground states of large systems to numerically study the critical behavior. To more fully characterize the transition we utilize free-fermionic representations of the renormalization group flows in the vicinity of the critical point, and point out possible connections with quantum infinite-randomness physics.   

Fermi surface reconstruction in the single band doped Hubbard model

We study the validity of Luttinger's theorem in the 2D repulsive Hubbard model, the parent Hamiltonian for cuprate superconductors, as a function of doping. Using determinant quantum Monte Carlo (DQMC) simulations, we compute the single-particle spectral functions and from its zero energy contour in momentum space, obtain the Fermi surface of the interacting system. This reveals the following: (1) With only nearest neighbor hopping, there is a Lifshitz transition at a critical doping, followed by continuous deviation from the Luttinger volume as one approaches the Mott Insulating limit, with deviations being maximal at the antinodal points. We will discuss the relation between Luttinger breaking Fermi surface and the T linear resistivity in transport. (2) Inclusion of a next nearest neighbor hopping that breaks particle-hole symmetry changes the continuous Fermi surface into Fermi pockets around the hot spot regions. It is important to note that we find Fermi surface restructuring at intermediate temperatures, where there is no spontaneous symmetry breaking. Deviation from the Luttinger count is also accompanied by an anomalous change in Seebeck coefficient.   

Universal conductivity at a 2d superconductor-insulator transition: the effects of quenched disorder and Coulomb interaction

We calculate the zero-temperature electrical conductivity at a superconductor-insulator transition in two spatial dimensions. We focus on transitions in the universality class of the dirty 3d XY model. We use a dual model consisting of a single Dirac fermion at zero density coupled to a Chern-Simons gauge field in the presence of a quenched random mass, with or without an unscreened Coulomb interaction. Our calculation is performed in a 1/Nf expansion, where Nf is the number of Dirac fermions.

At zeroth order, the model exhibits approximate particle-vortex self-dual electrical transport. Corrections of 1/Nf due to fluctuations in the Chern-Simons gauge field and disorder produce violations of self-duality. We find these violations would be supressed when the Coulomb interaction is present.   

Vertex Function in a Fermi Liquid near a q=0 Charge Quantum Critical Point

We analyze the vertex function for a two-dimensional Fermi liquid close to a q=0 charge quantum critical point (QCP). We show that there is an inconsistency in the calculation for the quasiparticle residue (Z) if one extracts Z from the one-loop self-energy and from the Ward identity, when one computes the vertex function within RPA. This inconsistency can be resolved if one includes an infinite series of ladder diagrams in the calculation of the vertex function. These diagrams are treated as zero within a conventional Fermi liquid theory with static interaction but are finite when using the renormalized, frequency and momentum dependent interaction. We demonstrate explicitly that including these terms changes the vertex function by a factor of Z^-1, which resolves the discrepancy between the two calculations.   

The critical point separating superconducting and incommensurate magnetic phases in CeCo0.5Rh0.5In5

We apply neutron diffraction as a function of magnetic field to access a critical point separating superconducting and incommensurate magnetic orders in CeCo_0.5Rh_0.5In₅.  At zero applied field, CeCo_0.5Rh_0.5In₅ displays both superconductivity (Tc=1.3 K) and spatially long-ranged commensurate antiferromagnetism (TN=3.5 K) with a propagation vector of  Q=(1/2, 1/2, 1/2).   On applying a magnetic field that suppresses the superconducting order parameter, the magnetic intensity scales as ~H/Hc2 ln (c/H) in the vortex phase, predicted for the response in close vicinity of quantum criticality owing to changes in the superconducting order parameter outside the vortex cores.  This critical point separates a superconducting phase from one that consists of coexisting superconducting and spin density wave phases.  In the low temperature field induced normal phase, an incommensurate magnetic order with propagation vector of  Q=(1/2, 1/2, 1/2+0.0055 r.l.u.) replaces the commensurate response present in the superconducting and vortex phases.  Metallic incommensurate order competes with intertwined unconventional superconductivity and commensurate magnetism in the ``115" superconductor series.   

Atomic Disorder Study in Ni alloys close to the Ferromagnetic Quantum Critical Point

This structural study, revealing the quality of selected Ni-alloys, Ni-V and Ni-Cr, aims to clarify the origin of magnetic clusters associated with the ferromagnetic-paramagnetic quantum phase transition driven by chemical substitution. Evidence for evolving magnetic clusters close to this disordered quantum critical point at a critical concentration xc=0.12 comes from muSR data [1] and recent neutron scattering data [2].

We present here a wide-angle neutron diffraction data and pair distribution function (PDF) analysis of both ferromagnetic Ni-alloys to check for the actual atomic distributions in polycrystalline samples prepared under different growth and annealing protocols.

Our PDF study uncovers that the atoms in Ni-V [3] and Ni-Cr are most likely randomly distributed on the lattice sites of the face-centered cubic (fcc) crystal structure for x<0.15. That confirms the ideal condition for a random distribution of “magnetic” clusters.

PDF data distinguish well simple random atom model from cluster and structure models. The results are sensitive to variation in the sample preparation and treatment. Only high temperature annealed samples yield the solid solution. Deviation from the protocol might lead to local inhomogeneities even to phase separation in Ni-Cr and Ni-V as demonstrated.

[1] R. Wang, A. Gebretsadik et al, “Quantum Griffiths phase inside the ferromagnetic phase in Ni_1-xV_x”, Phys Rev Lett 118, 267202 (2017)

[2] S. Bhattarai, H Adawi et al, “Evolution of short-range magnetic correlations in ferromagnetic Ni-V alloys”, Phys. Rev. B 107, 054409 (2023)

[3] A. Gebretsadik, et al, “Study of Atomic Disorder in Ni-V alloys”, arXiv:2302.1986, submitted to PRB   

Variational wavefunctions for topologically-ordered Fermi liquids

Quantum spin liquids provide a clear demonstration of topological order arising from magnetic frustration. These phases are most often studied in systems with localized spin-1/2 moments, where Gutzwiller-projected spinon wavefunctions can be effectively used to construct variational ansatzes for frustrated Heisenberg models. We generalize this procedure to allow for charge fluctuations - driven either through finite Hubbard repulsion or through doping - via the introduction of "ancilla" qubits, originally proposed in [Phys Rev R, 023172 (2020)]. We employ variational Monte Carlo techniques to calculate observables of these trial wavefunctions and optimize their energies against the two-dimensional Fermi-Hubbard model; in particular, we study the magnetic and charge correlations driven by the underlying spin liquid.