Fermi Surface Reconstruction without Symmetry Breaking

Open Access

Fermi Surface Reconstruction without Symmetry Breaking

Snir Gazit, Fakher F. Assaad, and Subir Sachdev

Phys. Rev. X 10, 041057 – Published 21 December 2020

Abstract

We present a sign-problem-free quantum Monte Carlo study of a model that exhibits quantum phase transitions without symmetry breaking and associated changes in the size of the Fermi surface. The model is an Ising gauge theory on the square lattice coupled to an Ising matter field and spinful “orthogonal” fermions at half filling, both carrying Ising gauge charges. In contrast to previous studies, our model hosts an electronlike, gauge-neutral fermion excitation providing access to Fermi-liquid phases. One of the phases of the model is a previously studied orthogonal semimetal, which has $Z_{2}$ topological order and Luttinger-volume-violating Fermi points with gapless orthogonal fermion excitations. We elucidate the global phase diagram of the model: Along with a conventional Fermi-liquid phase with a large Luttinger-volume Fermi surface, we also find a “deconfined” Fermi liquid in which the large Fermi surface coexists with fractionalized excitations. We present results for the electron spectral function, showing its evolution from the orthogonal semimetal with a spectral weight near momenta ${\pm π / 2, \pm π / 2}$ to a large Fermi surface.

Received 10 August 2020
Revised 5 October 2020
Accepted 16 October 2020

DOI:https://doi.org/10.1103/PhysRevX.10.041057

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Fermi surface Fractionalization Gauge theories Quantum phase transitions

Lattice gauge theory Quantum Monte Carlo

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Snir Gazit

Racah Institute of Physics and The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

Fakher F. Assaad

Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany, and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany

Subir Sachdev

Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

Popular Summary

Luttinger’s theorem predicts that the volume enclosed by a material’s Fermi surface—the mathematical boundary enclosing all occupied electron-momentum states—is directly tied to its fermion density. The only way to change that volume, according to Luttinger, is to break translational symmetry, that is, introduce a spatial modulation (such as a charge-density wave) with periodicity greater than that of a unit cell. But over the last couple of decades, observations of Fermi surface expansion in high-temperature superconductors and heavy fermion compounds have shown that this is not always the case. Here, we present a simple theoretical model to help explain these puzzling results.

From a theoretical perspective, a violation of Luttinger’s theorem requires introducing exotic quantum states in which electrons split into fractional particles. Our model realizes this scenario, which can be simulated using unbiased and numerically exact calculations. Indeed, with tuning of parameters, we demonstrate that electron fractionalization can mediate a Fermi-surface reconstruction that does not involve the breaking of translational symmetry.

Observations of a reduced Fermi volume without translational symmetry breaking would provide evidence of exotic topologically ordered states of matter. Our findings provide a guide for future analytical and theoretical studies of this intriguing phenomenon and may shed light on unsettled experimental results.

Key Image

Article Text

Click to Expand

References

Click to Expand

Issue

Vol. 10, Iss. 4 — October - December 2020

Subject Areas

Reuse & Permissions

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Lattice model of orthogonal fermions coupled to an Ising-Higgs lattice gauge theory. The matter fields $f_{r, α}$ (blue circle) and $τ_{r}^{z}$ (red circle) reside on the square lattice sites, and the Ising gauge field $σ_{r, η}^{z}$ (green square) is defined on the lattice bonds. (b) Global phase diagram of our model [Eqs. (2) and (3)] as a function of the hopping amplitude $t$ and transverse field $g$ . The phase boundaries are determined by the location of the confinement transition and emergence of $c$ fermions spectral weight; see the main text. Connecting lines are guides to the eye.
Reuse & Permissions
Figure 2
Orthogonal semimetal confinement transition. Evolution of the (a) flux susceptibility $χ_{B}$ and (b) staggered magnetization $M_{AFM}$ across the phase transition separating the OSM and the confined AFM as a function of the transverse field $g$ for a fixed hopping amplitude $t = 0.2$ . Different curves correspond to a set of increasing system sizes and inverse temperatures. $Δ_{AFM}$ is obtained through a extrapolation of the finite-size data to the thermodynamic limit.
Reuse & Permissions
Figure 3
Momentum-resolved $\tilde{Z} (k)$ , for a linear system size $L = 16$ and inverse temperature $β = 16$ , as a function of the hopping amplitude $t$ along two parameter cuts. (i) In (a)–(c), we fix $g = 0.55$ and cross the transition between the OSM and deconfined FL phases. Deep in the OSM phase, we find four maxima with a finite spectral weight centered about $k = {\pm π / 2, \pm π / 2}$ . With an increase in $t$ , a large diamond-shaped Fermi surface gradually appears upon approach to the deconfined FL phase. (ii) In (d) and (e), on the other hand, we set $g = 1.2$ and monitor the appearance of a Fermi surface, in the large $t$ limit, starting from a featureless low-energy spectrum deep in the confined AFM phase.
Reuse & Permissions
Figure 4
Phase transition between the OSM and deconfined FL phases as a function of $t$ for $g = 0.55$ . (a) Single-particle residue $\tilde{Z} (k)$ at the antinodal points. (b) Critical finite-size scaling of the superfluid stiffness $L ρ_{s}$ . (c) Staggered magnetization $M_{AFM}$ . $Δ_{AFM}$ is computed by an extrapolation to the thermodynamic limit. (d) Flux susceptibility $χ_{B}$ .
Reuse & Permissions
Figure 5
(a) Flux susceptibility $χ_{B}$ as a function of $g$ for $t = 3.0$ along the path connecting the confined and deconfined FL phases. (b) Single-particle residue $\tilde{Z} (k)$ evaluated at the antinodal point $k = {0, π}$ as a function of $t$ . Different curves correspond to different values of $g$ .
Reuse & Permissions
Figure 6
(a) Ising Landau gauge-fixing condition for the $π$ -flux lattice; black (red) bonds correspond to $σ_{b}^{z} = 1$ ( $- 1$ ). (b) Energy contours of the lower-band Dirac spectrum on the $π$ -flux lattice using the above gauge fixing. (c) Leading-order Feynman diagram for the physical fermion $c$ propagator $G_{c}^{β} (k, i ω_{m})$ . The bubble diagram evaluates to a convolution between the Ising matter field $ϕ^{z}$ and orthogonal fermion $f_{σ}$ propagators defined on the $π$ -flux lattice. (d) Finite-temperature spectral function $A (k, ω = 0)$ computed by a numerical evaluation of the bubble diagram.
Reuse & Permissions

Physical Review X