Non-Abelian topological insulators are characterized by matrix-valued,non-commuting topological charges with regard to more than one energy gap.Their descriptions go beyond the conventional topological band theory,in ...Non-Abelian topological insulators are characterized by matrix-valued,non-commuting topological charges with regard to more than one energy gap.Their descriptions go beyond the conventional topological band theory,in which an additive integer like the winding or Chern number is endowed separately with each(degenerate group of)energy band(s).In this work,we reveal that Floquet(time-periodic)driving could not only enrich the topology and phase transitions of non-Abelian topological matter,but also induce bulk-edge correspondence unique to nonequilibrium setups.Using a one-dimensional,three-band model as an illustrative example,we demonstrate that Floquet driving could reshuffle the phase diagram of the non-driven system,yielding both gapped and gapless Floquet band structures with non-Abelian topological charges.Moreover,by dynamically tuning the anomalous Floquet π-quasienergy gap,non-Abelian topological transitions inaccessible to static systems could arise,leading to much more complicated relations between non-Abelian topological charges and Floquet edge states.These discoveries put forth periodic driving as a powerful scheme of engineering non-Abelian topological phases and incubating unique non-Abelian band topology beyond equilibrium.展开更多
Let G be a finite abelian group and k be a positive integer.The Davenport constant is a central invariant in zero-sum thoery.The invariant Dk(G)generalizes the Davenport constant D(G)and is defined as the maximum leng...Let G be a finite abelian group and k be a positive integer.The Davenport constant is a central invariant in zero-sum thoery.The invariant Dk(G)generalizes the Davenport constant D(G)and is defined as the maximum length l such that there exists a sequenceB of length l overGcontaining k disjoint non-empty zero-sum subsequences.This paper studies the inverse problem associated with this invariant for the elementary abelian 2-groups C_(2)^(r).For r∈[2,4],we characterize the structures of zero-sum sequences of length D2(C_(2)^(r))and D2(C_(2)^(r))-1 in C_(2)^(r) that can be decomposed into at most two minimal zero-sum subsequences.For r∈[2,5],we characterize the structures of sequences of length D2(C_(2)^(r))-1.展开更多
In the lattice system,when the synthetic flux reaches aπphase along a closed loop under the synthetic gauge field,destructive interference occurs and gives rise to the localization phenomenon.This is known as the Aha...In the lattice system,when the synthetic flux reaches aπphase along a closed loop under the synthetic gauge field,destructive interference occurs and gives rise to the localization phenomenon.This is known as the Aharonov-Bohm(AB)caging effect.It provides a powerful tool for the study of quantum transport and dynamical effects.In the system where lattice sites possess internal structure and the underlying gauge field is non-Abelian,localization can also occur,forming the non-Abelian AB caging.Here,we propose an experimental scheme to synthesize non-Abelian gauge fields with a single trapped ion by coupling multiple internal levels and Fock states in its motion via laser fields.In contrast to the Abelian AB caging,we numerically observe that the non-Abelian AB caging occurs either when the interference matrix is nilpotent,or when the initial state is specifically set.Our experimental scheme broadens the study of localization phenomena and provides a novel tool for the study of non-Abelian physics.展开更多
Let K/Q be any abelian extension where Q is the field of rational numbers.By Galois theory and the Frobenius formula for induced characters,we prove that there exists a metabelian group G and an irreducible character ...Let K/Q be any abelian extension where Q is the field of rational numbers.By Galois theory and the Frobenius formula for induced characters,we prove that there exists a metabelian group G and an irreducible character X of G such that K=Q(X).展开更多
Gauge potential plays an important role in exploring exotic phenomena in the single- and many-body quantum systems.In this paper,we propose a scheme to create both new Abelian and non-Abelian gauge potentials by adiab...Gauge potential plays an important role in exploring exotic phenomena in the single- and many-body quantum systems.In this paper,we propose a scheme to create both new Abelian and non-Abelian gauge potentials by adiabatically controlling the degenerate Dicke model in cavity quantum electrodynamics.It is shown that a non-Abelian gauge potential is achieved only for a single atom,whereas an Abelianizen diagonal gauge potential is realized for the atomic ensemble.More importantly,two interesting quantum phenomena such as the geometric phase and the magnetic monopole induced by our created gauge potentials are also predicted.The possible physical realization is presented in the macroscopic circuit quantum electrodynamics with the Cooper pair boxes,which act as the artificial two-level atoms controlled by the gate voltage and the external magnetic flux.展开更多
we have discussed structures of Abelian group G by order |A(G) |of automoorphism group and have obtained all types of finite Abelian grooup G when the order of A(G) equals 27pq(p,q are odd primmes).
基金supported by the National Natural Science Foundation of China(Grant Nos.12275260 and 11905211)the Fundamental Research Funds for the Central Universities(Grant No.202364008)the Young Talents Project of Ocean University of China。
文摘Non-Abelian topological insulators are characterized by matrix-valued,non-commuting topological charges with regard to more than one energy gap.Their descriptions go beyond the conventional topological band theory,in which an additive integer like the winding or Chern number is endowed separately with each(degenerate group of)energy band(s).In this work,we reveal that Floquet(time-periodic)driving could not only enrich the topology and phase transitions of non-Abelian topological matter,but also induce bulk-edge correspondence unique to nonequilibrium setups.Using a one-dimensional,three-band model as an illustrative example,we demonstrate that Floquet driving could reshuffle the phase diagram of the non-driven system,yielding both gapped and gapless Floquet band structures with non-Abelian topological charges.Moreover,by dynamically tuning the anomalous Floquet π-quasienergy gap,non-Abelian topological transitions inaccessible to static systems could arise,leading to much more complicated relations between non-Abelian topological charges and Floquet edge states.These discoveries put forth periodic driving as a powerful scheme of engineering non-Abelian topological phases and incubating unique non-Abelian band topology beyond equilibrium.
基金supported by the National Natural Science Foundation of China(No.12301425)。
文摘Let G be a finite abelian group and k be a positive integer.The Davenport constant is a central invariant in zero-sum thoery.The invariant Dk(G)generalizes the Davenport constant D(G)and is defined as the maximum length l such that there exists a sequenceB of length l overGcontaining k disjoint non-empty zero-sum subsequences.This paper studies the inverse problem associated with this invariant for the elementary abelian 2-groups C_(2)^(r).For r∈[2,4],we characterize the structures of zero-sum sequences of length D2(C_(2)^(r))and D2(C_(2)^(r))-1 in C_(2)^(r) that can be decomposed into at most two minimal zero-sum subsequences.For r∈[2,5],we characterize the structures of sequences of length D2(C_(2)^(r))-1.
基金supported by the National Natural Science Foundation of China(Grant Nos.92165206,12275090,and 12304554)the Innovation Program for Quantum Science and Technology(Grant Nos.2021ZD0301603 and 2021ZD0302303)。
文摘In the lattice system,when the synthetic flux reaches aπphase along a closed loop under the synthetic gauge field,destructive interference occurs and gives rise to the localization phenomenon.This is known as the Aharonov-Bohm(AB)caging effect.It provides a powerful tool for the study of quantum transport and dynamical effects.In the system where lattice sites possess internal structure and the underlying gauge field is non-Abelian,localization can also occur,forming the non-Abelian AB caging.Here,we propose an experimental scheme to synthesize non-Abelian gauge fields with a single trapped ion by coupling multiple internal levels and Fock states in its motion via laser fields.In contrast to the Abelian AB caging,we numerically observe that the non-Abelian AB caging occurs either when the interference matrix is nilpotent,or when the initial state is specifically set.Our experimental scheme broadens the study of localization phenomena and provides a novel tool for the study of non-Abelian physics.
基金Supported by the National Program for the Basic Science Researches of China(G19990751)
文摘Let K/Q be any abelian extension where Q is the field of rational numbers.By Galois theory and the Frobenius formula for induced characters,we prove that there exists a metabelian group G and an irreducible character X of G such that K=Q(X).
基金Supported by the National Natural Science Foundation of China under Grant Nos.10904092,10934004,60978018,11074184,and 11074154the Zhejiang Provincial Natural Science Foundation under Grant No.Y6090001
文摘Gauge potential plays an important role in exploring exotic phenomena in the single- and many-body quantum systems.In this paper,we propose a scheme to create both new Abelian and non-Abelian gauge potentials by adiabatically controlling the degenerate Dicke model in cavity quantum electrodynamics.It is shown that a non-Abelian gauge potential is achieved only for a single atom,whereas an Abelianizen diagonal gauge potential is realized for the atomic ensemble.More importantly,two interesting quantum phenomena such as the geometric phase and the magnetic monopole induced by our created gauge potentials are also predicted.The possible physical realization is presented in the macroscopic circuit quantum electrodynamics with the Cooper pair boxes,which act as the artificial two-level atoms controlled by the gate voltage and the external magnetic flux.
文摘we have discussed structures of Abelian group G by order |A(G) |of automoorphism group and have obtained all types of finite Abelian grooup G when the order of A(G) equals 27pq(p,q are odd primmes).
