arXiv subjects

Rufus Boyack

Publications and source records attributed to Rufus Boyack.

At least 37 records · Page 2Linked to original sources

arXiv2021

Critical exponents for the valence-bond-solid transition in lattice quantum electrodynamics

Recent sign-problem-free quantum Monte Carlo simulations of (2+1)-dimensional lattice quantum electrodynamics (QED$_3$) with $N_f$ flavors of fermions on the square lattice have found evidence of continuous quantum phase transitions between a critical phase and a gapped valence-bond-solid (VBS) phase for flavor numbers $N_f=4$, $6$, and $8$. We derive the critical theory for these transitions, the chiral $O(2)$ QED$_3$-Gross-Neveu model, and show that the latter is equivalent to the gauged Nambu--Jona-Lasinio model. Using known large-$N_f$ results for the latter, we estimate the order parameter anomalous dimension and the correlation length exponent for the transitions mentioned above. We obtain large-$N_f$ results for the dimensions of fermion bilinear operators, in both the gauged and ungauged chiral $O(2)$ Gross-Neveu models, which respectively describe the long-distance power-law decay of two-particle correlation functions at the VBS transition in lattice QED$_3$ and the Kekulé-VBS transition for correlated fermions on the honeycomb lattice.

cond-mat.str-el↗

arXiv2020

The functional-integral approach to Gaussian fluctuations in Eliashberg theory

The Eliashberg theory of superconductivity is based on a dynamical electron-phonon interaction as opposed to a static interaction present in BCS theory. The standard derivation of Eliashberg theory is based on an equation of motion approach, which incorporates certain approximations such as Migdal's approximation for the pairing vertex. In this paper we provide a functional-integral-based derivation of Eliashberg theory and we also consider its Gaussian-fluctuation extension. The functional approach enables a self-consistent method of computing the mean-field equations, which arise as saddle-point conditions, and here we observe that the conventional Eliashberg self energy and pairing function both appear as Hubbard-Stratonovich transformations. An important consequence of this fact is that it provides a systematic derivation of the Cooper and density-channel interactions in the Gaussian fluctuation response. We also investigate the strong-coupling fluctuation diamagnetic susceptibility near the critical temperature.

cond-mat.supr-con↗

arXiv2020

The bound-state solutions of the one-dimensional hydrogen atom

The one-dimensional hydrogen atom is an intriguing quantum mechanics problem that exhibits several properties which have been continually debated. In particular, there has been variance as to whether or not even-parity solutions exist, and specifically whether or not the ground state is an even-parity state with infinite negative energy. We study a "regularized" version of this system, where the potential is a constant in the vicinity of the origin, and we discuss the even- and odd-parity solutions for this regularized one-dimensional hydrogen atom. We show how the even-parity states, with the exception of the ground state, converge to the same functional form and become degenerate for $x > 0$ with the odd-parity solutions as the cutoff approaches zero. This differs with conclusions derived from analysis of the singular (i.e., without regularization) one-dimensional Coulomb potential, where even-parity solutions are absent from the spectrum.

quant-ph↗

arXiv2020

Thermodynamics of Eliashberg theory in the weak-coupling limit

The weak-coupling limits of the gap and critical temperature computed within Eliashberg theory surprisingly deviate from the BCS theory predictions by a factor of $1/\sqrt{e}$. Interestingly, however, the ratio of these two quantities agrees for both theories. Motivated by this result, here we investigate the weak-coupling thermodynamics of Eliashberg theory, with a central focus on the free energy, specific heat, and the critical magnetic field. In particular, we numerically calculate the difference between the superconducting and normal-state specific heats, and we find that this quantity differs from its BCS counterpart by a factor of $1/\sqrt{e}$, for all temperatures below $T_{c}$. We find that the dimensionless ratio of the specific-heat discontinuity to the normal-state specific heat reduces to the BCS prediction given by $ΔC_{V}(T_{c})/C_{V,n}(T_c)\approx1.43$. This gives further evidence to the expectation that all dimensionless ratios tend to their "universal values" in the weak-coupling limit.

cond-mat.supr-con↗

arXiv2020

Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics

Elucidating the phase diagram of lattice gauge theories with fermionic matter in 2+1 dimensions has become a problem of considerable interest in recent years, motivated by physical problems ranging from chiral symmetry breaking in high-energy physics to fractionalized phases of strongly correlated materials in condensed matter physics. For a sufficiently large number $N_f$ of flavors of four-component Dirac fermions, recent sign-problem-free quantum Monte Carlo studies of lattice quantum electrodynamics (QED$_3$) on the square lattice have found evidence for a continuous quantum phase transition between a power-law correlated conformal QED$_3$ phase and a confining valence-bond-solid phase with spontaneously broken point-group symmetries. The critical continuum theory of this transition was shown to be the $O(2)$ QED$_3$-Gross-Neveu model, equivalent to the gauged Nambu-Jona-Lasinio model, and critical exponents were computed to first order in the large-$N_f$ expansion and the $ε$ expansion. We extend these studies by computing critical exponents to second order in the large-$N_f$ expansion and to four-loop order in the $ε$ expansion below four spacetime dimensions. In the latter context, we also explicitly demonstrate that the discrete $\mathbb{Z}_4$ symmetry of the valence-bond-solid order parameter is dynamically enlarged to a continuous $O(2)$ symmetry at criticality for all values of $N_f$.

cond-mat.str-el↗

arXiv2020

Restoring gauge invariance in conventional fluctuation corrections to a superconductor

The complete set of diagrams for conventional fluctuation corrections to the normal state of an ultraclean superconductor is derived using the functional-integral approach. The standard diagrams which characterize the fluctuation phase of a superconductor, namely, Aslamazov-Larkin, Maki-Thompson, and Density of States, are obtained and proved to be insufficient to produce a gauge-invariant electromagnetic response. An additional diagram is derived, and it is found to be essential for resolving a problematic and underappreciated aspect of the conventional fluctuation formalism. It is only with the inclusion of this additional diagram that the theory is now rendered gauge invariant and does not display a normal-state Meissner effect. It is shown that not only the Aslamazov-Larkin term but all of the microscopic diagrams are encapsulated within a Gaussian-level treatment of the effective action.

cond-mat.supr-con↗

arXiv2019

Critical properties of the Néel/algebraic-spin-liquid transition

The algebraic spin liquid is a long-sought-after phase of matter characterized by the absence of quasiparticle excitations, a low-energy description in terms of emergent Dirac fermions and gauge fields interacting according to (2+1)D quantum electrodynamics (QED$_3$), and power-law correlations with universal exponents. The prototypical algebraic spin liquid is the Affleck-Marston $π$-flux phase, originally proposed as a possible ground state of the spin-1/2 Heisenberg model on the 2D square lattice. While the latter model is now known to order antiferromagnetically at zero temperature, recent sign-problem-free quantum Monte Carlo simulations of spin-1/2 fermions coupled to a compact U(1) gauge field on the square lattice have shown that quantum fluctuations can destroy Néel order and drive a direct quantum phase transition to the $π$-flux phase. We show this transition is in the universality class of the chiral Heisenberg QED$_3$-Gross-Neveu-Yukawa model with a single SU(2) doublet of four-component Dirac fermions (i.e., $N_f=1$), pointing out important differences with the corresponding putative transition on the kagome lattice. Using an $ε$ expansion below four spacetime dimensions to four-loop order, and a large-$N_f$ expansion up to second order, we show the transition is continuous and compute various thermodynamic and susceptibility critical exponents at this transition, setting the stage for future numerical determinations of these quantities. As a byproduct of our analysis, we also obtain charge-density-wave and valence-bond-solid susceptibility exponents at the semimetal-Néel transition for interacting fermions on the honeycomb lattice.

cond-mat.str-el↗

arXiv2019

Eliashberg theory in the weak-coupling limit: results on the real frequency axis

We formulate and solve the Eliashberg equations on the imaginary frequency axis at temperatures below $T_c$ in the weak-coupling limit. We find an excellent scaling at all temperatures, for a given coupling strength, and the normalized order parameter exhibits a BCS-like temperature dependence. The hybrid real-imaginary axis equations are also solved to obtain numerically exact analytic continuations from the imaginary frequency axis to the real frequency axis. This provides a determination of the gap edge, which, in the weak-coupling limit, is identical to the order parameter from the imaginary axis. The analytical result for the zero-temperature gap edge deviates from the BCS result by a factor of $1/\sqrt{e}$, which was also obtained for the transition temperature $T_c$. We show that the normalized gap function on both the real and imaginary frequency axes, for an electron-phonon Einstein spectrum ($δ$-function) of a given strength, is a universal function of frequency, independent of temperature. The $1/\sqrt{e}$ correction is a result of this non-trivial frequency dependence in the gap function. This modification, in the gap edge and in $T_{c}$, serves to preserve various dimensionless ratios to their BCS values.

cond-mat.supr-con↗

arXiv2019

Electromagnetic response of superconductors in the presence of multiple collective modes

We revisit the importance of collective-mode fluctuations and gauge invariance in the electromagnetic response of superconducting systems. In particular, we show that order-parameter fluctuations, gapless or not, have no contribution to the Meissner effect in both $s$- and $p$-wave superconductors. More generally, we extend this result to uniform and nonuniform superfluids with no external wavevector scale. To facilitate this analysis, we formulate a path-integral-based matrix methodology for computing the electromagnetic response of fermionic fluids in the presence of concomitantly fluctuating collective modes. Closed-form expressions for the electromagnetic response in different scenarios are provided, including the case of fluctuations of electronic density and the phase and amplitude of the order parameter. All microscopic symmetries and invariances are manifestly satisfied in our formalism, and it can be straightforwardly extended to other scenarios.

cond-mat.supr-con↗

arXiv2019

Deconfined criticality in the QED$_{3}$ Gross-Neveu-Yukawa model: The $1/N$ expansion revisited

The critical properties of the QED$_{3}$ Gross-Neveu-Yukawa (GNY) model in 2+1 dimensions with $N$ flavors of two-component Dirac fermions are computed to first order in the $1/N$ expansion. For the specific case of $N=2$, the critical point is conjectured to be dual to the Néel-to-valence-bond-solid (VBS) deconfined critical point of quantum antiferromagnets on the square lattice. It is found that Aslamazov-Larkin diagrams, missed by previous $ε$- and $1/N$-expansion studies with four-component fermions, give important contributions to the scaling dimensions of various operators. With the inclusion of these diagrams, the resummed scaling dimensions of the adjoint fermion bilinear and scalar field at the QED$_{3}$ GNY critical point are in reasonable agreement with numerical studies of the Néel-to-VBS transition, in support of the duality conjecture.

cond-mat.str-el↗

arXiv2018

Combined effects of pairing fluctuations and a pseudogap in the Cuprate Hall effect

The normal-state behavior of the temperature-dependent Hall coefficient in cuprate superconductors is investigated using linear response theory. The Hall conductivity is of paramount importance in that its sign and magnitude directly reflect the sign of the charge carriers and the size of particle-hole asymmetry effects. Here we apply a strong-pairing fluctuation theory that incorporates pseudogap effects known to be important in cuprate transport. As a result, in the vicinity of the transition temperature our theoretical approach goes beyond the conventional superconducting fluctuation formalism. In this regime, pseudogap effects are evident in both the transverse and longitudinal conductivities and the bosonic response is explicitly gauge invariant. The presence of a gap in the excitation spectrum is also apparent at higher temperatures, where the gapped fermionic quasiparticles are the dominant contribution to the Hall coefficient. The observed non-monotonic temperature dependence of the Hall coefficient therefore results from a delicate interplay between the fermionic quasiparticles and the bosonic fluctuations. An important feature of our work is that the sign of the Hall conductivity from the Cooper pair fluctuations is the same as that of their fermionic constituents. Thus, we find no sign change in the Hall coefficient above the transition temperature. This prediction is corroborated by experiments, away from special charge ordering stoichiometries. The theoretical results presented in this paper provide crucial signatures that can be experimentally verified, enabling validation of the present theory.

cond-mat.supr-con↗

arXiv2018

Critical behavior of the QED$_3$-Gross-Neveu-Yukawa model at four loops

We study the universal critical properties of the QED$_3$-Gross-Neveu-Yukawa model with $N$ flavors of four-component Dirac fermions coupled to a real scalar order parameter at four-loop order in the $ε$ expansion below four dimensions. For $N=1$, the model is conjectured to be infrared dual to the $SU(2)$-symmetric noncompact $\mathbb{C}$P$^1$ model, which describes the deconfined quantum critical point of the Néel-valence-bond-solid transition of spin-1/2 quantum antiferromagnets on the two-dimensional square lattice. For $N=2$, the model describes a quantum phase transition between an algebraic spin liquid and a chiral spin liquid in the spin-1/2 kagomé antiferromagnet. For general $N$ we determine the order parameter anomalous dimension, the correlation length exponent, the stability critical exponent, as well as the scaling dimensions of $SU(N)$ singlet and adjoint fermion mass bilinears at the critical point. We use Padé approximants to obtain estimates of critical properties in 2+1 dimensions.

cond-mat.str-el↗

arXiv2018

Transition between algebraic and $\mathbb{Z}_2$ quantum spin liquids at large $N$

We present a field theory description of a quantum phase transition in two spatial dimensions between a $U(1)$ algebraic spin liquid with $N$ flavors of gapless two-component Dirac fermionic spinons and a gapped $\mathbb{Z}_2$ spin liquid. This transition is driven by spinon pairing and concomitant Higgsing of the emergent $U(1)$ gauge field. For sufficiently large $N$ we find a quantum critical point with non-Gaussian exponents that is stable against instanton proliferation. We compute critical exponents using either $1/N$ or $ε$ expansions, and give estimates of the critical value of $N$ below which the quantum critical point disappears.

cond-mat.str-el↗

arXiv2017

Cuprate diamagnetism in the presence of a pseudogap: Beyond the standard fluctuation formalism

It is often claimed that among the strongest evidence for preformed-pair physics in the cuprates are the experimentally observed large values for the diamagnetic susceptibility and Nernst coefficient. These findings are most apparent in the underdoped regime, where a pseudogap is also evident. While the conventional (Gaussian) fluctuation picture has been applied to address these results, this preformed-pair approach omits the crucial effects of a pseudogap. In this paper we remedy this omission by computing the diamagnetic susceptibility and Nernst coefficient in the presence of a normal state gap. We find a large diamagnetic response for a range of temperatures much higher than the transition temperature. In particular, we report semi-quantitative agreement with the measured diamagnetic susceptibility onset temperatures, over the entire range of hole dopings. Notable is the fact that at the lower critical doping of the superconducting dome, where the transition temperature vanishes and the pseudogap onset temperature remains large, the onset temperature for both diamagnetic and transverse thermoelectric transport coefficients tends to zero. Due to the importance attributed to the cuprate diamagnetic susceptibility and Nernst coefficient, this work helps to clarify the extent to which pairing fluctuations are a component of the cuprate pseudogap.

cond-mat.str-el↗

arXiv2017

Exact correlation functions in the cuprate pseudogap phase: combined effects of charge order and pairing

There is a multiplicity of charge ordered, pairing-based or pair density wave theories of the cuprate pseudogap, albeit arising from different microscopic mechanisms. For mean field schemes (of which there are many) we demonstrate here that they have precise implications for two body physics in the same way that they are able to address the one body physics of photoemission spectroscopy. This follows because the full vertex can be obtained exactly from the Ward-Takahashi identity. As an illustration, we present the spin response functions, finding that a recently proposed pair density wave (Amperean pairing) scheme is readily distinguishable from other related scenarios.

cond-mat.supr-con↗

arXiv2017

Collective mode contributions to the Meissner effect: Fulde-Ferrell and pair-density wave superfluids

In this paper we demonstrate the necessity of including the generally omitted collective mode contributions in calculations of the Meissner effect for non-uniform superconductors. We consider superconducting pairing with non-zero center of mass momentum, as is relevant to high transition temperature cuprates, cold atoms, and quantum chromodynamic superconductors. For the concrete example of the Fulde-Ferrell phase we present a quantitative calculation of the superfluid density, showing the collective mode contributions are not only appreciable but that they derive from the amplitude mode of the order parameter. This latter mode (related to the Higgs mode in a charged system) is generally viewed as being invisible in conventional superconductors. However, our analysis shows that it is extremely important in pair-density wave type superconductors, where it destroys superfluidity well before the mean-field order parameter vanishes.

cond-mat.supr-con↗

arXiv2016

Two-dimensional spin-imbalanced Fermi gases at non-zero temperature: Phase separation of a non-condensate

We study a trapped two-dimensional spin-imbalanced Fermi gas over a range of temperatures. In the moderate temperature regime, associated with current experiments, we find reasonable semi-quantitative agreement with the measured density profiles as functions of varying spin imbalance and interaction strength. Our calculations show that, in contrast to the three-dimensional case, the phase separation which appears as a spin balanced core, can be associated with non-condensed fermion pairs. We present predictions at lower temperatures where a quasi-condensate will first appear, based on the pair momentum distribution and following the protocols of Jochim and collaborators. While these profiles also indicate phase separation, they exhibit distinctive features which may aid in identifying the condensation regime.

cond-mat.quant-gas↗

arXiv2016

Gauge invariant theories of linear response for strongly correlated superconductors

We present a general diagrammatic theory for determining consistent electromagnetic response functions in strongly correlated fermionic superfluids. The general treatment of correlations beyond BCS theory requires a new theoretical formalism not contained in the current literature. Among concrete examples are a rather extensive class of theoretical models which incorporate BCS-BEC crossover as applied to the ultra cold Fermi gases, along with theories specifically associated with the high-$T_c$ cuprates. The challenge is to maintain gauge invariance, while simultaneously incorporating additional self-energy terms arising from strong correlation effects. Central to our approach is the application of the Ward-Takahashi identity, which introduces collective mode contributions in the response functions and guarantees that the $f$-sum rule is satisfied. We outline a powerful and very general method to determine these collective modes in a manner compatible with gauge invariance. Finally, as an alternative approach, we contrast with the path integral formalism. Here, the calculation of gauge invariant response appears more straightforward. However, the collective modes introduced are essentially those of strict BCS theory, with no modification from correlation effects. Since the path integral scheme simultaneously addresses electrodynamics and thermodynamics, we emphasize that it should be subjected to a consistency test beyond gauge invariance, namely that of the compressibility sum-rule. We show how this sum-rule fails in the conventional path integral approach.

cond-mat.supr-con↗