arXiv subjects

Fadi Sun

Publications and source records attributed to Fadi Sun.

At least 19 recordsLinked to original sources

arXiv2025

Dominant Excitonic Superconductivity in a Three-component Hubbard Chain

Understanding superconductivity emerging from repulsive fermions remains a major challenge in condensed matter physics. In this paper, we investigate the pairing tendencies in a one-dimensional, three component repulsive Hubbard model, using the density matrix renormalization group method. At half-filling, the system exhibits density wave ground state due to strong Hubbard repulsions. Upon doping, we find that Cooper pairs can emerge, whose fluctuations predominate the long-range physics in the system across a wide parameter range. The effective attractions between Cooper pairs are mediated by the particle-hole fluctuations in the third non-pairing component, resembling an excitonic mechanism of superconductivity. The coexistence of multiple density waves and superconductivity at different fermion fillings is explored. We also present an analytical study of the pairing mechanism in both weak and strong coupling limits. Our results provide a new perspective for understanding and exploring unconventional superconductivities in strongly correlated fermionic systems.

cond-mat.supr-con↗

arXiv2025

Nonperturbative quantum field theory for pseudo-Goldstone modes, slow-Goldstone modes, and their quantum chaos

In this work, we develop a novel form of non-perturbative theory to identify a light pseudo-Goldstone mode with a small mass, as well as a new type of Goldstone mode with a tiny slope (termed the slow-Goldstone mode), which may not be obtained via traditional perturbative methods. We demonstrate our formalism in the context of superfluids formed by Rashba spin-orbit coupled spinor bosons in a square lattice weakly interacting with a spin-anisotropic interaction. The experimental detections of these two modes, especially their roles leading to the quantum information scramblings at a finite temperature are discussed. The slow-Goldstone mode is compared with the slow light and the soft mode in the Sachdev-Ye-Kitaev models. This non-perturbative formalism can be widely applied to study other emergent particles in various quantum matter.

cond-mat.quant-gas↗

arXiv2023

Bose-Einstein condensations of magnons in quantum magnets with spin-orbit coupling in a Zeeman field

We study the response of a quantum magnet with spin-orbit coupling (SOC) to a Zeeman field by constructing effective actions and performing Renormalization Group (RG) analysis. There are several novel classes of quantum phase transitions at a low $ h_{c1} $ and an upper critical field $ h_{c2} $ driven by magnon condensations at commensurate (C-) or in-commensurate (IC-) momenta $ 0 < k_0 < \pi $. The intermediate IC- Skyrmion crystal (IC-SkX) phase is controlled by a line of fixed points in the RG flows labeled by $ k_0 $. We derive the relations between the quantum spin and the order parameters of the effective actions which determine the spin-orbital structures of the IC-SkX phase. We also analyze the operator contents near $ h_{c1} $ and $ h_{c2} $ which determine the exotic excitation spectra inside the IC-SkX. The intrinsic differences between the magnon condensations at the C- and IC- momenta are explored. The two critical fields $ h_{c1} < h_{c2} $ and the intermediate IC-SkX phase could be a generic feature to any quantum magnets with SOC in a Zeeman field. Experimental implications to some materials or cold atom systems with SOC in a Zeeman field are presented.

cond-mat.str-el↗

arXiv2023

Topological phase transitions generated by the order from quantum disorder

The order from quantum disorder (OFQD) phenomenon was first discovered in quantum spin systems in geometric frustrated lattice. Similar phenomenon was also discovered in interacting bosonic systems or quantum spin systems with spin-orbit coupling in a bipartite lattice. Here we show that the OFQD also leads to a topological phase transition. We demonstrate this new connection in the experimentally realized weakly interacting Quantum Anomalous Hall system of spinor bosons in an optical lattice. There are two classes of topological phenomena: the first class is a perturbative one smoothly connected to the non-interacting limit. The second one is a non-perturbative one which has no analog in the non-interacting limit. Their experimental detections are also discussed.

cond-mat.quant-gas↗

arXiv2023

Topological phase transitions, invariants and enriched bulk-edge correspondences in fermionic gapless systems with extended Fermi surface

Topological phases and topological phase transitions (TPT) are among the most fantastic phenomena in Nature. Here we show that injecting a current may lead to new topological phases, especially new gapless topological metallic phases with extended Fermi surfaces (FSs) through novel class of TPTs in the bulk or the boundary. Specifically, we study the quantum anomalous Hall (QAH) system in a square lattice under various forms of injecting currents. In addition to the previously known Chern insulator (which will be called even Chern insulator here), band insulator and band metal (BM), we find three new topological phases we name as: the gapped odd Chern insulator (Odd CI), the gapless odd Chern metal (Odd CM) and even Chern metal (Even CM). The Chern number may not be effective anymore in characterizing the topological gapless phases with extended FS. It is the Hall conductance which acts as the new topological invariant in such gapless systems. Its jump is a universal integer or non-integer across the even CM/BM or odd CM/BM TPT respectively where there is also a corresponding TPT in the Longitudinal (L-)edge modes. The Odd/even CM to BM transition is a novel class of TPT without any non-analyticity in the ground state energy density. This presents the first example of a TPT which is not a quantum phase transition (QPT). The original bulk-edge correspondence is enriched into bulk/Longitudinal (L-)/Transverse (T-) edge correspondence. The L-edge reconstruction may happen earlier, later or at the same time as the bulk TPT respectively in the even CI/odd CI/odd CM sequence with the edge dynamic exponent $ z_L=3 $, in the even CI/even CM/odd CM sequence with $ z_L=2 $ or a direct even CI/odd CM with a flat edge. The disappearance of the T-edge always happen at the same time as the bulk TPT with a universal edge critical behaviour.

cond-mat.mes-hall↗

arXiv2022

Quantum Lifshitz transitions generated by order from quantum disorder in strongly correlated Rashba spin-orbital coupled systems

We study the system of strongly interacting spinor bosons in a square lattice subject to the isotropic Rashba SOC $ \alpha=\beta $. It supports collinear spin-bond correlated magnetic Y-x phase, a gapped in-commensurate (IC-) co-planar IC-XY-y phase, a non-coplanar commensurate (C-) $ 3 \times 3 $ Skyrmion crystal phase (SkX). The state at the Abelian point $ \alpha=\beta=\pi/2 $ is just an AFM state in a rotated basis. Slightly away from the point, we identify a spurious $ U(1) $ symmetry, develop a novel and non-perturbative method to calculate not only the gap, but also the excitation spectrum due to the order from quantum disorder (OFQD) mechanism. We construct a symmetry based effective action to investigate the quantum Lifshitz transition from the Y-x state to the IC-XY-y state and establish the connection between the phenomenological parameters in the effective action and those evaluated by the microscopic non-perturbative OFQD analysis in the large $ S $ limits. Experimental implications on cold atoms and some 4d or 5d Kitaev materials are discussed.

cond-mat.str-el↗

arXiv2020

Response of a strongly interacting spin-orbit coupling system to a Zeeman field

A strongly spin-orbital coupled systems could be in a magnetic ordered phase at zero field. However, a Zeeman field could drive it into different quantum or topological phases. In this work, starting from general symmetry principle, we construct various effective actions to study all these quantum phases and phase transitions which take different forms depending on the condensation momenta are commensurate or in-commensurate. We not only recover all these quantum phases and their excitations achieved by the microscopic calculations, but also discover several novel classes of quantum phase transitions with dynamic exponents $ z=1, z=2 $ and anisotropic ones $ (z_x=3/2, z_y=3) $ respectively. We determine the relations between the quantum spin and the order parameters of the effective actions which display rich spin-orbital structures. We find a new type of dangerously irrelevant operator we name type-II, in distinction from the known one we name type-I. We explore a new phenomena called order parameter fractionization where one complex order parameter split into two which is different than quantum spin fractionization into a spinon and a $ Z_2 $ flux. Finite temperature transitions are presented. The dynamic spin-spin correlation functions are evaluated. Thermal Hall conductivities are discussed. The cases with the $ U(1)_{soc} $ symmetry explicitly broken are briefly outlined. In view of recent experimental advances in generating 2d SOC for cold atoms in optical lattices, these new many-body phenomena can be explored in the near future cold atom experiments. Implications to various SOC materials such as MnSi, Fe$_{0.5}$Co$_{0.5}$Si, especially 4d Kitaev materials $\alpha$-RuCl$_3$ in a Zeeman field are outlined.

cond-mat.str-el↗

arXiv2020

Quantum spin liquids in a square lattice subject to an Abelian flux

We report that a possible Z2 quantum spin liquid (QSL) can be observed in a new class of frustrated system: spinor bosons subject to a pi flux in a square lattice. We construct a new class of Ginsburg-Landau (GL) type of effective action to classify possible quantum or topological phases at any coupling strengths. It can be used to reproduce the frustrated SF with the 4 sublattice $ 90^{\circ} $ coplanar spin structure plus its excitations in the weak coupling limit and the FM Mott plus its excitations in the strong coupling limit achieved in our previous work. It also establishes deep and intrinsic connections between the GL effective action and the order from quantum disorder (OFQD) phenomena in the weak coupling limit. Most importantly, it predicts two possible new phases at intermediate couplings: a FM SF phase or a frustrated magnetic Mott phase. We argue that the latter one is more likely and melts into a $ Z_2 $ quantum spin liquid (QSL) phase. If the heating issue can be under a reasonable control at intermediate couplings $ U/t \sim 1 $, the topological order of the $ Z_2 $ QSL maybe uniquely probed by the current cold atom or photonic experimental techniques.

cond-mat.str-el↗

arXiv2019

Periodic Table of SYK and supersymmetric SYK

We develop a systematic and unified random matrix theory to classify Sachdev-Ye-Kitaev (SYK) and supersymmetric (SUSY) SYK models and also work out the structure of the energy levels in one periodic table. The SYK with even $q$- and SUSY SYK with odd $q$-body interaction, $N$ even or odd number of Majorana fermions are put on the same footing in the minimal Hilbert space, $N\pmod 8$ and $q\pmod 4$ double Bott periodicity are identified. Exact diagonalizations are performed to study both the bulk energy level statistics and hard edge behaviours. A new moment ratio of the smallest positive eigenvalue is introduced to determine hard edge index efficiently. Excellent agreements between the ED results and the symmetry classifications are demonstrated. Our complete and systematic methods can be transformed to map out more complicated periodic tables of SYK models with more degree of freedoms, tensor models and symmetry protected topological phases. Possible classification of charge neutral quantum black holes are hinted.

cond-mat.str-el↗

arXiv2019

Nearly order from quantum disorder phenomena and its observation in a bosonic quantum anomalous Hall system

We report a new many body phenomena called " Nearly order from quantum disorder phenomena" (NOFQD). We demonstrate the NOFQD in the experimentally realized weakly interacting Quantum Anomalous Hall system of spinor bosons in an optical lattice. We establish intrinsic connections between the phenomenological GL theory and the microscopic calculations on the effective potential. Connections with the bilayer quantum Hall system with a total filling factor $ \nu_T=1 $ are made. Some insightful analogy with $ NAdS_2/NCFT_1 $ ( where $ N $ also means nearly ) correspondence in the context of Sachdev-Ye-Kitaev models are hinted. Two types of OFQDs are classified, one response trivially, another non-trivially to a small deformation to the Hamiltonian leading to NOFQD. The NOFQD can be detected in the current cold atom bosonic quantum anomalous Hall experiments and may also appear in many other frustrated systems.

cond-mat.quant-gas↗

arXiv2019

Classification of the quantum chaos in colored Sachdev-Ye-Kitaev models

The random matrix theory (RMT) can be used to classify both topological phases of matter and quantum chaos. We develop a systematic and transformative RMT to classify the quantum chaos in the colored Sachdev-Ye-Kitaev (SYK) model first introduced by Gross and Rosenhaus. Here we focus on the 2-colored case and 4-colored case with balanced number of Majorana fermion $N$. By identifying the maximal symmetries, the independent parity conservation sectors, the minimum (irreducible) Hilbert space, and especially the relevant anti-unitary and unitary operators, we show that the color degree of freedoms lead to novel quantum chaotic behaviours. When $N$ is odd, different symmetry operators need to be constructed to make the classifications complete. The 2-colored case only show 3-fold Wigner-Dyson way, and the 4-colored case show 10-fold generalized Wigner-Dyson way which may also have non-trivial edge exponents. We also study 2- and 4-colored hybrid SYK models which display many salient quantum chaotic features hidden in the corresponding pure SYK models. These features motivate us to develop a systematic RMT to study the energy level statistics of 2 or 4 un-correlated random matrix ensembles. The exact diagonalizations are performed to study both the bulk energy level statistics and the edge exponents and find excellent agreements with our exact maximal symmetry classifications. Our complete and systematic methods can be easily extended to study the generic imbalanced cases. They may be transferred to the classifications of colored tensor models, quantum chromodynamics with pairings across different colors, quantum black holes and interacting symmetry protected (or enriched) topological phases.

cond-mat.str-el↗

arXiv2018

A new universal ratio in Random Matrix Theory and chaotic to integrable transition in Type-I and Type-II hybrid Sachdev-Ye-Kitaev models

We investigate chaotic to integrable transition in two types of hybrid SYK models which contain both $ q=4 $ SYK with interaction $ J $ and $ q=2 $ SYK with an interaction $ K $ in type-I or $(q=2)^2$ SYK with an interaction $ \sqrt{K} $ in type-II. These models include hybrid Majorana fermion, complex fermion and bosonic SYK. For the Majorana fermion case, we discuss both $ N $ even and $ N $ odd case. We make exact symmetry analysis on the possible symmetry class of both types of hybrid SYK in the 10 fold way by Random Matrix Theory (RMT) and also work out the degeneracy of each energy levels. We introduce a new universal ratio which is the ratio of the next nearest neighbour (NNN) energy level spacing to characterize the RMT. We perform exact diagonalization to evaluate both the known NN ratio and the new NNN ratio, then use both ratios to study Chaotic to Integrable transitions (CIT) in both types of hybrid SYK models. Some preliminary results on possible quantum analog of Kolmogorov-Arnold-Moser (KAM) theorem and its dual version in the quantum chaotic side are given. We explore some intrinsic connections between the two complementary approaches to quantum chaos: the RMT and the Lyapunov exponent by the $ 1/N $ expansion in the large $ N $ limit at a suitable temperature range. Comments on some previously related works are given. Some future perspectives, especially the failure of the Zamoloddchikov's c-theorem in 1d CFT RG flow are outlined.

cond-mat.str-el↗

arXiv2017

Frustrated superfluids in a non-Abelian flux

We study possible superfluid states of the Rashba spin-orbit coupled (SOC) spinor bosons with the spin anisotropic interaction $ \lambda $ hopping in a square lattice. The frustrations from the non-abelian flux due to the SOC leads to novel spin-bond correlated superfluids. By using a recently developed systematic "order from quantum disorder" analysis, we not only determine the true quantum ground state, but also evaluate the mass gap in the spin sector at $ \lambda < 1 $, especially compute the the excitation spectrum of the Goldstone mode in the spin sector at $ \lambda=1 $ which would be quadratic without the analysis. The analysis also leads to different critical exponents on the two sides of the 2nd order transition driven by a roton touchdown at $ \lambda=1 $. The intimate analogy at $ \lambda=1 $ with the charge neutral Goldstone mode in the pseudo-spin sector in the Bilayer quantum Hall systems at the total filling factor $ \nu_T=1 $ are stressed. The experimental implications and detections of these novel phenomena in cold atoms loaded on a optical lattice are presented.

cond-mat.quant-gas↗

arXiv2017

Symmetry protected bosonic topological phase transitions: Quantum Anomalous Hall system of weakly interacting spinor bosons in a square lattice

We study possible many body phenomena in the Quantum Anomalous Hall system of weakly interacting spinor bosons in a square lattice. There are various novel spin-bond correlated superfluids (SF) and quantum or topological phase transitions among these SF phases. One transition is a first order one driven by roton droppings ( but with non-zero gaps $ \Delta_R $ ) tuned by the Zeeman field $ h $. Another is a second order bosonic Lifshitz transition with the dynamic exponents $ z_x=z_y=2 $ and an accompanying $ [C_4 \times C_4]_D $ symmetry breaking. It is driven by the softening of the superfluid Goldstone mode tuned by the ratio of spin-orbit coupled (SOC) strength over the hopping strength. The two phase boundaries meet at a topological tri-critical (TT) point which separates the $ h=0 $ line into two SF phases with $ N=2 $ and $ N=4 $ condensation momenta respectively. At the $ h=0 $ line where the system has an anti-unitary $ Z_2 $ Reflection symmetry, there are infinite number of classically degenerate family of states on both sides. We perform a systematic order from quantum disorder analysis to find the quantum ground states, also calculate the roton gaps $ \Delta_R $ generated by the order from disorder mechanism on both sides of the TT point. The $ N=2 $ and $ N=4 $ SF phases have the same spin-orbital XY-AFM spin structure, respect the anti-unitary symmetry and break the $ [C_4 \times C_4]_D $ symmetry, so they be distinguished only by the different topology of the BEC condensation momenta instead of by any differences in the symmetry breaking patterns. All these novel quantum or topological phenomena can be probed in the recent experimentally realized weakly interacting Quantum Anomalous Hall (QAH) model of $ ^87 Rb $ by Wu, {\sl et.al}, Science 354, 83-88 (2016).

cond-mat.quant-gas↗

arXiv2017

Slow-Goldstone mode generated by order from quantum disorder and its experimental detection

The order from quantum disorders (OFQD) phenomenon is well-known and ubiquitous in particle physics and frustrated magnetic systems. Typically, OFQD transfers a spurious Goldstone mode into a pseudo-Goldstone mode with a tiny gap. Here, we report an opposite phenomenon: OFQD transfers a spurious quadratic mode into a true linear Goldstone mode with a very small velocity (named slow-Goldstone mode). This new phenomenon is demonstrated in an interacting bosonic system subjected to an Abelian flux. We develop a new and systematic OFQD analysis to determine the true quantum ground state and the whole excitation spectrum. In the weak-coupling limit, the superfluid ground state has a 4-sublattice 90? coplanar spin structure, which supports 4 linear Goldstone modes with 3 different velocities. One of which is generated by the OFQD is much softer than the other 3 Goldstone modes, so it can be easily detected in the cold atom or photonic experiments. In the strong-coupling limit, the ferromagnetic Mott ground state with a true quadratic Goldstone mode. We speculate that there could be some topological phases intervening between the two symmetry broken states. These novel phenomena may be observed in the current cold-atom or photonic experiments subjected to an Abelian flux at the weak coupling limit where the heatings may be well under control. Possible connections to Coleman-Weinberg potential in particle physics, 1/N expansion of Sachdev-Ye-Kitaev models, and zero temperature quantum black hole entropy are outlined.

cond-mat.quant-gas↗

arXiv2016

Topological depletions and sub-leading scalings across topological phase transitions

It remains an open problem if there are universal scaling functions across a topological quantum phase transition (TPT) without an order parameter, but with extended Fermi surfaces (FS ). Here, we study a simple system of fermions hopping in a cubic lattice subject to a Weyl type spin-orbit coupling (SOC). As one tunes the SOC parameter at the half filling, the system displays Weyl fermions and also various TPT due to the collision of particle-particle or hole-hole Weyl Fermi Surface (WFS). At the zero temperature, the TPT is found to be a third order one whose critical exponent is determined. We derive the scaling functions of the specific heat, compressibility and magnetic susceptibilities. In contrast to all the previous cases in quantum or topological transitions, although the leading terms are non-universal and cutoff dependent, the sub-leading terms satisfy universal scaling relations. The sub-leading scaling leads to the topological depletions (TD) which show non-analytic and non-Fermi liquid corrections in the quantum critical regime, can be easily distinguished from the analytic leading terms and detected experimentally. One can also form a topological Wilson ratio from the TD of two conserved quantities such as the specific heat and the compressibility. As a byproduct, we also find Type II Weyl fermions appearing as the TPT due to the collision of the extended particle-hole WFS. Experimental realizations and detections in cold atom systems and materials with SOC are discussed.

cond-mat.str-el↗

arXiv2016

High Chern number topological superfluids and new class of topological phase transitions of Rashba spin-orbit coupled fermions on a lattice

Searching for the first topological superfluid (TSF) remains a primary goal of modern science. Here we study the system of attractively interacting fermions hopping in a square lattice with any linear combinations of Rashba or Dresselhaus spin-orbit coupling (SOC) in a normal Zeeman field. By imposing self-consistence equations at half filling, we find there are 3 phases: Band insulator ( BI ), Superfluid (SF) and Topological superfluid (TSF) with a Chern number $ C=2 $. The $ C=2 $ TSF happens in small Zeeman fields and weak interactions which is in the experimentally most easily accessible regime. The transition from the BI to the SF is a first order one due to the multi-minima structure of the ground state energy landscape. There is a new class of topological phase transition from the SF to the $ C=2 $ TSF at the low critical field $ h_{c1} $, then another one from the $ C=2 $ TSF to the BI at the upper critical field $ h_{c2} $. We derive effective actions to describe the two new classes of topological phase transitions, then use them to study the Majorana edge modes and the zero modes inside the vortex core of the $ C=2 $ TSF near both $ h_{c1} $ and $ h_{c2} $, especially explore their spatial and spin structures. We find the edge modes decay into the bulk with oscillating behaviors and determine both the decay and oscillating lengths. We compute the bulk spectra and map out the Berry Curvature distribution in momentum space near both $ h_{c1} $ and $ h_{c2} $. We also elaborate some intriguing bulk-Berry curvature-edge-vortex correspondences. Experimental implications in both 2d non-centrosymmetric materials under a periodic substrate and cold atoms in an optical lattice are given.

cond-mat.quant-gas↗

arXiv2016

Two classes of organization principle: quantum/topological phase transitions meet complete/in-complete devil staircases and their experimental realizations

There exists many quantum or topological phases in Nature. One well known organization principle is through various quantum or topological phases transitions between or among these phases. Another is through either complete or in-complete devil staircases in their quantized forms. Here, we show that both classes of organization principle appear in an experimentally accessible system: strongly interacting spinor bosons subject to any of the linear combinations of the Rashba and Dresselhaus spin-orbit coupling (SOC) in the space of the two SOC parameters $ ( \alpha, \beta) $ in a square lattice. In the strong coupling limit, it leads to a new quantum spin model called Rotated Ferromagnetic Heisenberg model (RFHM). The RFHM leads to rich and unconventional magnetic phases even in a bipartite lattice. For the first class, by identifying a suitable low energy mode, we investigate a new quantum Lifshitz transition from the Y-x to the IC-SkX-y phase. For the second class, we introduce the topological rational and irrational winding numbers $ W $ to characterize the incomplete or complete devil staircases and also perform their quantizations. The IC-YZ-x/LQx phases form a Cantor set with a fractal dimension along the complete devil staircase. They also take most of measures in the incomplete devil staircases when $ \beta \ll \alpha $. Quantum chaos and quantum information scramblings along the diagonal line $ \alpha=\beta $ are discussed. Implications on un-conventional magnetic ordered phases detected in the 4d- or 5d-orbital strongly correlated materials with SOC and in the current or near future cold atom systems are presented.

cond-mat.quant-gas↗