arXiv subjects

Dan Mao

Publications and source records attributed to Dan Mao.

26 records · Page 2Linked to original sources

arXiv2020

From $p$-adic to Archimedean Physics: Renormalization Group Flow and Berkovich Spaces

We introduce the $p$-adic particle-in-a-box as a free particle with periodic boundary conditions in the $p$-adic spatial domain. We compute its energy spectrum, and show that the spectrum of the Archimedean particle-in-a-box can be recovered from the $p$-adic spectrum via an Euler product formula. This product formula arises from a flow equation in Berkovich space, which we interpret as a space of theories connected by a kind of renormalization group flow. We propose that Berkovich spaces can be used to relate $p$-adic and Archimedean quantities generally.

hep-th↗

arXiv2019

Spin Liquids and Pseudogap Metals in $SU(4)$ Hubbard Model in Moiré Superlattice

Motivated by the realization of spin-valley Hubbard on triangular moiré superlattice in ABC trilayer graphene aligned with hexagon boron nitride (hBN) and possibly also in twisted transition metal dichalcogenide homobilayers, we study possible Mott insulating phases and pseudogap metals based on symmetry constraint and parton mean field theories. First we show that Luttinger constraint allows two distinct symmetric and featureless Fermi liquids when there is an inter-valley Hund's term breaking $SU(4)$ spin rotation. Especially, there exists a symmetric and featureless "pseudogap metal" with small Fermi surfaces. Then we suggest to search for such an unconventional metallic state by doping the Mott insulator at $ν_T=2$. For this purpose, we study the $ν_T=2$ Mott insulator using $SO(6)$ Schwinger boson or Schwinger fermion parton. At the $SU(4)$ symmetric point, we find two symmetric $Z_2$ spin liquids. With a large anti inter-valley Hund's term, a featureless Mott insulator is natural. Next we show that doping the featureless Mott insulator or a $Z_2$ spin liquid can lead to featureless or orthogonal "pseudogap metal" with small Fermi surfaces proportional to the doping. Besides, we also provide one scenario for the evolution from "pseudogap metal" to the conventional Fermi liquid through an intermediate exotic "deconfined metal" phase. Last, we give brief comments on the possibility of $U(1)$ spinon fermi surface state or $Z_4$ spin liquid at $ν_T=1$.

cond-mat.str-el↗

arXiv2019

Slow scrambling and hidden integrability in a random rotor model

We analyze the out-of-time-order correlation functions of a solvable model of a large number, $N$, of $M$-component quantum rotors coupled by Gaussian-distributed random, infinite-range exchange interactions. We focus on the growth of commutators of operators at a temperature $T$ above the zero temperature quantum critical point separating the spin-glass and paramagnetic phases. In the large $N,~M$ limit, the squared commutators of the rotor fields do not display any exponential growth of commutators, in spite of the absence of any sharp quasiparticle-like excitations in the disorder-averaged theory. We show that in this limit, the problem is integrable and point out interesting connections to random-matrix theory. At leading order in $1/M$, there are no modifications to the critical behavior but an irrelevant term in the fixed-point action leads to a small exponential growth of the squared commutator. We also introduce and comment on a generalized model involving $p$-pair rotor interactions.

cond-mat.str-el↗

arXiv2019

Twisted Bilayer Graphene Aligned with Hexagonal Boron Nitride: Anomalous Hall Effect and a Lattice Model

A recent experiment reported a large anomalous Hall effect in Magic Angle Twisted Bilayer Graphene (TBG) aligned with a hexagonal boron nitride(h-BN) substrate at $\frac{3}{4}$ filling of the conduction band. In this paper we study this system theoretically, and propose explanations of this observation. We emphasize that the physics for this new system is qualitatively different from the pure TBG system. The aligned h-BN breaks in-plane two-fold rotation symmetry and gaps out the Dirac crossings of ordinary TBG. The resulting valence and conduction bands of each valley carry equal and opposite Chern numbers $C=\pm 1$. A useful framework is provided by a lattice extended Hubbard model for this system which we derive. An obvious possible explanation of the anomalous Hall effect is that at $3/4$-filling the system is a spin-valley polarized ferromagnetic insulator where the electrons completely fill a Chern band. We also examine an alternate more radical proposal of a compressible valley polarized but spin unpolarized composite ferm liquid metallic state. We argue that either state is compatible with current experiments, and propose ways to distinguish between them in the future. We also briefly discuss the physics at $1/2$ filling.

cond-mat.str-el↗

arXiv2018

Nearly Flat Chern Bands in Moiré Superlattices

Topology and electron interactions are two central themes in modern condensed matter physics. Here we propose graphene based systems where both the band topology and interaction effects can be simply controlled with electric fields. We study a number of systems of twisted double layers with small twist angle where a moiré super-lattice is formed. Each layer is chosen to be either AB stacked bilayer graphene (BG), ABC stacked trilayer graphene (TG), or hexagonal boron nitride (h-BN). In these systems a vertical applied electric field enables control of the bandwidth, and interestingly also the Chern number. We find that the Chern numbers of the bands associated with each of the two microscopic valleys can be $\pm 0,\pm 1,\pm 2, \pm 3$ depending on the specific system and vertical electrical field. We show that these graphene moiré super-lattices are promising platforms to realize a number of fascinating many-body phenomena, including (Fractional) Quantum Anomalous Hall Effects. We also discuss conceptual similarities and implications for modeling twisted bilayer graphene systems.

cond-mat.str-el↗

arXiv2016

Quantum Phase Transitions Between Bosonic Symmetry Protected Topological States Without Sign Problem: Nonlinear Sigma Model with a Topological Term

We propose a series of simple $2d$ lattice interacting fermion models that we demonstrate at low energy describe bosonic symmetry protected topological (SPT) states and quantum phase transitions between them. This is because due to interaction the fermions are gapped both at the boundary of the SPT states and at the bulk quantum phase transition, thus these models at low energy can be described completely by bosonic degrees of freedom. We show that the bulk of these models is described by a Sp($N$) principal chiral model with a topological $Θ$-term, whose boundary is described by a Sp($N$) principal chiral model with a Wess-Zumino-Witten term at level-1. The quantum phase transition between SPT states in the bulk is tuned by a particular interaction term, which corresponds to tuning $Θ$ in the field theory, and the phase transition occurs at $Θ= π$. The simplest version of these models with $N=1$ is equivalent to the familiar O(4) nonlinear sigma model (NLSM) with a topological term, whose boundary is a $(1+1)d$ conformal field theory with central charge $c = 1$. After breaking the O(4) symmetry to its subgroups, this model can be viewed as bosonic SPT states with U(1), or $Z_2$ symmetries, etc. All these fermion models including the bulk quantum phase transitions can be simulated with determinant Quantum Monte Carlo method without the sign problem. Recent numerical results strongly suggests that the quantum disordered phase of the O(4) NLSM with precisely $Θ= π$ is a stable $(2+1)d$ conformal field theory (CFT) with gapless bosonic modes.

cond-mat.str-el↗

arXiv2009

The Solar-Interior Equation of State with the Path-Integral Formalism I. Domain of Validity

This is the first paper in a series that deals with solar-physics applications of the equation-of-state formalism based on the formulation of the so-called "Feynman-Kac (FK) representation". Here, the FK equation of state is presented and adapted for solar applications. Its domain of validity is assessed. The practical application to the Sun will be dealt with in Paper II. Paper III will extend the current FK formalism to a higher order. Use of the FK equation of state is limited to physical conditions for which more than 90% of helium is ionized. This incudes the inner region of the Sun out to about .98 of the solar radius. Despite this limitation, in the parts of the Sun where it is applicable, the FK equation of state has the power to be more accurate than the equations of state currently used in solar modeling. The FK approach is especially suited to study physical effects such as Coulomb screening, bound states, the onset of recombination of fully ionized species, as well as diffraction and exchange effects. The localizing power of helioseismology allows a test of the FK equation of state. Such a test will be beneficial both for better solar models and for tighter solar constraints of the equation of state.

astro-ph↗

arXiv2009

Dynamic screening in solar plasma

In the hot, dense plasma of solar and stellar interiors, Coulomb potentials are screened, resulting in increased nuclear reaction rates. Although Salpeter's approximation for static screening is widely accepted and used in stellar modeling, the question of screening in nuclear reactions has been revisited. In particular the issue of dynamic effects has been raised by Shaviv and Shaviv who apply the techniques of molecular dynamics to the conditions in the Sun's core in order to numerically determine the effect of screening. By directly calculating the motion of ions and electrons due to Coulomb interactions, the simulations are used to compute the effect of screening without the mean-field assumption inherent in Salpeter's approximation. In this paper we reproduce their numerical analysis of the screening energy in the plasma of the solar core and conclude that the effects of dynamic screening are relevant and should be included when stellar nuclear reaction rates are computed.

astro-ph.SR↗