arXiv subjects

Matthias Punk

Publications and source records attributed to Matthias Punk.

At least 19 recordsLinked to original sources

arXiv2021

Projective symmetry group classification of chiral $\mathbb{Z}_2$ spin liquids on the pyrochlore lattice: application to the spin-$1/2$ XXZ Heisenberg model

We give a complete classification of fully symmetric as well as chiral $\mathbb{Z}_2$ quantum spin liquids on the pyrochlore lattice using a projective symmetry group analysis of Schwinger boson mean-field states. We find 50 independent ans\"atze, including the 12 fully symmetric nearest-neighbor $\mathbb{Z}_2$ spin liquids that have been classified by Liu et al. [https://journals.aps.org/prb/abstract/10.1103/PhysRevB.100.075125]. For each class we specify the most general symmetry-allowed mean-field Hamiltonian. Additionally, we test the properties of a subset of the spin liquid ans\"atze by solving the mean-field equations for the spin-$1/2$ XXZ model near the antiferromagnetic Heisenberg point. We find four chiral spin liquids that break the screw symmetry of the lattice modulo time reversal symmetry. These states have a different symmetry than the previously studied monopole flux state and their unique characteristic is a $\frac{\pi}{3}$ flux enclosed by every rhombus of the lattice.

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arXiv2021

Quenched disorder at antiferromagnetic quantum critical points in $2d$ metals

We study spin density wave quantum critical points in two dimensional metals with a quenched disorder potential coupling to the electron density. Adopting an $\epsilon$-expansion around three spatial dimensions, where both disorder and the Yukawa-type interaction between electrons and bosonic order parameter fluctuations are marginal, we present a perturbative, one-loop renormalization group analysis of this problem, where the interplay between fermionic and bosonic excitations is fully incorporated. Considering two different Gaussian disorder models restricted to small-angle scattering, we show that the non-Fermi liquid fixed point of the clean SDW hot-spot model is generically unstable and the theory flows to strong coupling due to a mutual enhancement of interactions and disorder. We study properties of the asymptotic flow towards strong coupling, where our perturbative approach eventually breaks down. Our results indicate that disorder dominates at low energies, suggesting that the ground-state in two dimensions is Anderson-localized.

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arXiv2020

Multiloop pseudofermion functional renormalization for quantum spin systems: Application to the spin-$\frac{1}{2}$ kagome Heisenberg model

We present a multiloop pseudofermion functional renormalization group (pffRG) approach to quantum spin systems. As a test case, we study the spin-$\tfrac{1}{2}$ Heisenberg model on the kagome lattice, a prime example of a geometrically frustrated magnet believed to host a quantum spin liquid. Our main physical result is that, at pure nearest-neighbor coupling, the system shows indications for an algebraic spin liquid through slower-than-exponential decay with distance for the static spin susceptibility, while the pseudofermion self-energy develops intriguing low-energy features. Methodologically, the pseudofermion representation of spin models inherently yields a strongly interacting system, and the quantitative reliability of a truncated fRG flow is \textit{a priori} unclear. Our main technical result is the demonstration of convergence in loop number within multiloop pffRG. Through correspondence with the self-consistent parquet equations, this provides further evidence for the internal consistency of the approach. The loop order required for convergence of the pseudofermion vertices is rather large, but the spin susceptibility is more benign, appearing almost fully converged for loop orders $\ell \geq 5$. The multiloop flow remains stable as the infrared cutoff $\Lambda$ is reduced relative to the microscopic exchange interaction $J$, allowing us to reach values of $\Lambda/J$ on the subpercent level in the spin-liquid phase. By contrast, solving the parquet equations via direct fixed-point iteration becomes increasingly difficult for low $\Lambda/J$. We also scrutinize the pseudofermion constraint of single occupation per site, which is only fulfilled on average in pffRG, by explicitly computing fermion-number fluctuations. Although the latter are not entirely suppressed, we find that they do not affect the qualitative conclusions drawn from the spin susceptibility.

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arXiv2020

A slave boson description of pseudogap metals in t-J models

We present a simple modification of the standard U(1) slave boson construction for the single band t-J model which accounts for two-particle bound states of spinons and holons. This construction naturally gives rise to fractionalized Fermi liquid ground states, featuring small, hole-like pocket Fermi surfaces with an anisotropic quasiparticle weight in the absence of broken symmetries. In a specific parameter regime our approach maps the square lattice t-J model to a generalized quantum dimer model, which was introduced as a toy model for the metallic pseudogap phase in hole-doped cuprates in [PNAS 112,9552-9557 (2015)]. Our slave boson construction captures essential features of the nodal-antinodal dichotomy and straightforwardly describes sharp, Fermi arc-like features in the electron spectral function. Moreover, it allows to study quantum phase transitions between fractionalized Fermi liquid phases and superconductors or ordinary Fermi liquids.

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arXiv2019

Solvable lattice models for metals with Z2 topological order

We present quantum dimer models in two dimensions which realize metallic ground states with Z2 topological order. Our models are generalizations of a dimer model introduced in [PNAS 112,9552-9557 (2015)] to provide an effective description of unconventional metallic states in hole-doped Mott insulators. We construct exact ground state wave functions in a specific parameter regime and show that the ground state realizes a fractionalized Fermi liquid. Due to the presence of Z2 topological order the Luttinger count is modified and the volume enclosed by the Fermi surface is proportional to the density of doped holes away from half filling. We also comment on possible applications to magic-angle twisted bilayer graphene.

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arXiv2019

Incommensurate $2k_F$ density wave quantum criticality in two dimensional metals

We revisit the problem of two dimensional metals in the vicinity of a quantum phase transition to incommensurate $\mathbf{Q}=2k_F$ charge density wave order, where the order parameter wave vector $\mathbf{Q}$ connects two hot spots on the Fermi surface with parallel tangents. Earlier theoretical works argued that such critical points are potentially unstable, if the Fermi surface at the hot spots is not sufficiently flat. Here we perform a controlled, perturbative renormalization group analysis and find a stable fixed point corresponding to a continuous quantum phase transition, which exhibits a strong dynamical nesting of the Fermi surface at the hot spots. We derive scaling forms of correlation functions at the critical point and discuss potential implications for experiments with transition metal dichalcogenides and rare-earth tellurides.

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arXiv2018

Signatures of correlated magnetic phases in the local two-particle density matrix

Experiments with quantum gas microscopes have started to explore the antiferromagnetic phase of the two-dimensional Fermi-Hubbard model and effects of doping with holes away from half filling. In this work we show how direct measurements of the system averaged two-spin density matrix and its full counting statistics can be used to identify different correlated magnetic phases with or without long-range order. We discuss examples of phases which are potentially realized in the Hubbard model close to half filling, including antiferrromagnetically ordered insulators and metals, as well as insulating spin-liquids and metals with topological order. For these candidate states we predict the doping- and temperature dependence of local correlators, which can be directly measured in current experiments.

cond-mat.quant-gas↗

arXiv2018

Aging dynamics in quenched noisy long-range quantum Ising models

We consider the $d$-dimensional transverse-field Ising model with power-law interactions $J/r^{d+\sigma}$ in the presence of a noisy longitudinal field with zero average. We study the longitudinal-magnetization dynamics of an initial paramagnetic state after a sudden switch-on of both the interactions and the noisy field. While the system eventually relaxes to an infinite-temperature state with vanishing magnetization correlations, we find that two-time correlation functions show aging at intermediate times. Moreover, for times shorter than the inverse noise strength $\kappa$ and distances longer than $a(J/\kappa)^{2/\sigma}$ with $a$ being the lattice spacing, we find a critical scaling regime of correlation and response functions consistent with the model A dynamical universality class with an initial-slip exponent $\theta=1$ and dynamical critical exponent $z=\sigma/2$. We obtain our results analytically by deriving an effective action for the magnetization field including the noise in a non-perturbative way. The above scaling regime is governed by a non-equilibrium fixed point dominated by the noise fluctuations.

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arXiv2017

Exact solution of a two-species quantum dimer model for pseudogap metals

We present an exact ground state solution of a quantum dimer model introduced in Ref.[1], which features ordinary bosonic spin-singlet dimers as well as fermionic dimers that can be viewed as bound states of spinons and holons in a hole-doped resonating valence bond liquid. Interestingly, this model captures several essential properties of the metallic pseudogap phase in high-$T_c$ cuprate superconductors. We identify a line in parameter space where the exact ground state wave functions can be constructed at an arbitrary density of fermionic dimers. At this exactly solvable line the ground state has a huge degeneracy, which can be interpreted as a flat band of fermionic excitations. Perturbing around the exactly solvable line, this degeneracy is lifted and the ground state is a fractionalized Fermi liquid with a small pocket Fermi surface in the low doping limit.

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arXiv2017

Non-Fermi liquid at the FFLO quantum critical point

When a 2D superconductor is subjected to a strong in-plane magnetic field, Zeeman polarization of the Fermi surface can give rise to inhomogeneous FFLO order with a spatially modulated gap. Further increase of the magnetic field eventually drives the system into a normal metal state. Here, we perform a renormalization group analysis of this quantum phase transition, starting from an appropriate low-energy theory recently introduced by Piazza et al. (Ref.1). We compute one-loop flow equations within the controlled dimensional regularization scheme with fixed dimension of Fermi surface, expanding in $\epsilon = 5/2 - d$. We find a new stable non-Fermi liquid fixed point and discuss its critical properties. One of the most interesting aspects of the FFLO non-Fermi liquid scenario is that the quantum critical point is potentially naked, with the scaling regime observable down to arbitrary low temperatures. In order to study this possibility, we perform a general analysis of competing instabilities, which suggests that only charge density wave order is enhanced in the vicinity of the quantum critical point.

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arXiv2017

Electron spectral functions in a quantum dimer model for topological metals

We study single electron spectral functions in a quantum dimer model introduced by Punk, Allais and Sachdev (Ref. [1]). The Hilbert space of this model is spanned by hard-core coverings of the square lattice with two types of dimers: ordinary bosonic spin-singlets, as well as fermionic dimers carrying charge +e and spin 1/2, which can be viewed as bound-states of spinons and holons in a doped resonating valence bond (RVB) liquid. This model realizes a metallic phase with topological order and captures several properties of the pseudogap phase in hole-doped cuprates, such as a reconstructed Fermi surface with small hole-pockets and a highly anisotropic quasiparticle residue in the absence of any broken symmetries. Using a combination of exact diagonalization and analytical methods we compute electron spectral functions and show that this model indeed exhibits a sizeable antinodal pseudogap, with a momentum dependence deviating from a simple d-wave form, in accordance with experiments on underdoped cuprates.

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arXiv2017

Deconfined quantum criticality in SU(3) antiferromagnets on the triangular lattice

We propose field theories for a deconfined quantum critical point in $SU(3)$ antiferromagnets on the triangular lattice. In particular we consider the continuous transition between a magnetic, three- sublattice color-ordered phase and a trimerized $SU(3)$ singlet phase. Starting from the magnetically ordered state we derive a critical theory in terms of fractional bosonic degrees of freedom, in close analogy to the well-developed description of the $SU(2)$ Neel - valence bond solid (VBS) transition on the square lattice. Our critical theory consists of three coupled $CP^2$ models and we study its fixed point structure using a functional renormalization group approach in a suitable large $N$ limit. We find a stable critical fixed point and estimate its critical exponents, thereby providing an example of deconfined criticality beyond the universality class of the $CP^N$ model. In addition we present a complementary route towards the critical field theory by studying topological defects of the trimerized $SU(3)$ singlet phase.

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arXiv2016

Quantum spin liquid ground states of the Heisenberg-Kitaev model on the triangular lattice

We study quantum disordered ground states of the two dimensional Heisenberg-Kitaev model on the triangular lattice using a Schwinger boson approach. Our aim is to identify and characterize potential gapped quantum spin liquid phases that are stabilized by anisotropic Kitaev interactions. For antiferromagnetic Heisenberg- and Kitaev couplings and sufficiently small spin $S$ we find three different symmetric $Z_2$ spin liquid phases, separated by two continuous quantum phase transitions. Interestingly, the gap of elementary excitations remains finite throughout the transitions. The first spin liquid phase corresponds to the well known zero-flux state in the Heisenberg limit, which is stable with respect to small Kitaev couplings and develops $120^\circ$ order in the semi-classical limit at large $S$. In the opposite Kitaev limit we find a different spin liquid ground-state, which is a quantum disordered version of a magnetically ordered state with antiferromagnetic chains, in accordance with results in the classical limit. Finally, at intermediate couplings we find a spin liquid state with unconventional spin correlations. Upon spinon condensation this state develops Bragg peaks at incommensurate momenta in close analogy to the magnetically ordered Z2 vortex crystal phase, which has been analyzed in recent theoretical works.

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arXiv2016

Spin structure factors of chiral quantum spin liquids on the kagome lattice

We calculate dynamical spin structure factors for gapped chiral spin liquid states in the spin-1/2 Heisenberg antiferromagnet on the kagome lattice using Schwinger-boson mean-field theory. In contrast to static (equal-time) structure factors, the dynamical structure factor shows clear signatures of time-reversal symmetry breaking for chiral spin liquid states. In particular, momentum inversion $\bm{k} \to -\bm{k}$ symmetry as well as the six-fold rotation symmetry around the $\Gamma$-point are lost. We highlight other interesting features, such as a relatively flat onset of the two-spinon continuum for the \emph{cuboc1} state. Our work is based on the projective symmetry group classification of time-reversal symmetry breaking Schwinger-boson mean-field states by Messio, Lhuillier, and Misguich.

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arXiv2016

Finite temperature scaling close to Ising-nematic quantum critical points in two-dimensional metals

We study finite temperature properties of metals close to an Ising-nematic quantum critical point in two spatial dimensions. In particular we show that at any finite temperature there is a regime where order parameter fluctuations are characterized by a dynamical critical exponent $z=2$, in contrast to $z=3$ found at zero temperature. Our results are based on a simple Eliashberg-type approach, which gives rise to a boson self-energy proportional to $\Omega/\gamma(T)$ at small momenta, where $\gamma(T)$ is the temperature dependent fermion scattering rate. These findings might shed some light on recent Monte-Carlo simulations at finite temperature, where results consistent with $z=2$ were found.

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arXiv2015

Nematic fluctuations and their wave vector in two-dimensional metals

We revisit the problem of electrons on a square lattice below half filling close to an Ising-nematic quantum critical point. For Fermi surfaces with sufficiently strong antinodal nesting, the static nematic susceptibility is maximal at the antinodal nesting wave vector within a simple RPA calculation. We present a detailed analysis of the nematic susceptibility within Eliashberg theory and show that the strong interaction between Fermions in the antinodal regions shifts the maximum of the nematic susceptibility to slightly larger wave vectors. The corresponding order is akin to the incommensurate charge-density wave with d-wave form factor found recently in some underdoped cuprate materials. At sufficiently high temperatures around $T/t \sim 0.1$ nematic fluctuations are strongest at zero wave vector.

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arXiv2015

A quantum dimer model for the pseudogap metal

We propose a quantum dimer model for the metallic state of the hole-doped cuprates at low hole density, $p$. The Hilbert space is spanned by spinless, neutral, bosonic dimers and spin $S=1/2$, charge $+e$ fermionic dimers. The model realizes a `fractionalized Fermi liquid' with no symmetry-breaking and small hole pocket Fermi surfaces enclosing a total area determined by $p$. Exact diagonalization, on lattices of sizes up to $8 \times 8$, shows anisotropic quasiparticle residue around the pocket Fermi surfaces. We discuss the relationship to experiments.

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arXiv2014

Dynamical preparation of laser-excited anisotropic Rydberg crystals in 2D optical lattices

We describe the dynamical preparation of anisotropic crystalline phases obtained by laser-exciting ultracold Alkali atoms to Rydberg p-states where they interact via anisotropic van der Waals interactions. We develop a time- dependent variational mean field ansatz to model large, but finite two-dimensional systems in experimentally accessible parameter regimes, and we present numerical simulations to illustrate the dynamical formation of anisotropic Rydberg crystals.

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