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### TG3.2: Strongly correlated condensed matter and cold atom systems

**I. Coordinator:**

chung@mail.nctu.edu.tw

**II. Core Members:**

__Center Scientists__

Prof. Chung-Hou Chung (NYCU)

Prof. Daw-Wei Wang (NTHU)

Prof. Chien-Te Wu (NYCU)

Prof. Daw-Wei Wang (NTHU)

Prof. Chien-Te Wu (NYCU)

__Core members__

Prof. Sungkit Yip (AS)

Prof. Daw-Wei Wang (NTHU)

Prof. Chien-Te Wu (NYCU)

Prof. Shin-Ming Huang (NSYSU)

Prof. Yi-Ping Huang (NTHU)

Prof. Po-Yao Chang (NTHU)

Prof. Jhih-Shih You (NTNU)

Prof. Shang-Huw Jen (AS)

Prof. Chang-Tse Hsieh (NTU)

Prof. Daw-Wei Wang (NTHU)

Prof. Chien-Te Wu (NYCU)

Prof. Shin-Ming Huang (NSYSU)

Prof. Yi-Ping Huang (NTHU)

Prof. Po-Yao Chang (NTHU)

Prof. Jhih-Shih You (NTNU)

Prof. Shang-Huw Jen (AS)

Prof. Chang-Tse Hsieh (NTU)

__Postdocs__

Dr. Po-Hao Chou

Dr. Yung-Yeh Chang

**III. Research Themes:**

(1) Correlation driven topological phases of matter and Majorana fermions

The discovery of symmetry protected topological insulators around 2005 has led to an enormous effort in trying to realize more exotic topological material phases both theoretically and experimentally, including: topological insulators, topological superconductors, Dirac and Weyl semimetals. Spin-orbit couplings and specific symmetries of the systems play crucial roles in supporting these non-trivial topological and superconductivity properties. The most exciting phenomena of these topological materials are the gapless edge (surface) states protected by certain symmetries. Of particular interest are topological superconductors that support gapless self-conjugate, charge-neutral fermionic quasi-particle excitations.

These excitations which reflect non-trivial topological bulk properties are localized at the edges, known as Majorana fermions (MFs). Due to the robustness and non-Abelian statistics, MFs have been proposed to be an attractive candidate for realizing quantum bit (qbit) in building quantum computers. Much effort has been put in searching for signatures of Majorana fermions in solid-state materials. There have been possible signatures of MFs in metal-semiconductor wire hetero-structure. Extensive studies have been put to search for the topological states due to geometry or crystal symmetries in non-interacting or weakly interacting electron systems. More recently, interest has been shifted to search for topological phases and Majorana fermions induced by electron correlations. The strong electron correlations may induce and

stabilize the topological phases. Currently, we are interested in correlation driven topological state of matter.

(2) Novel quantum phases, quantum phase transitions in and out of equilibrium

In many-body condensed matter systems, strong electron correlations often lead to novel and exotic quantum ground states (or quantum phases), such as: Mott insulators, unconventional metallic and superconductivity in heavy-fermions and in cuprates, exotic spin-liquid phases in frustrated magnets

Among them, the most challenging open problem is the understanding of the phase diagram of high-Tc cuprate superconductors, in particular the pseudogap phase at low hole doping of cuprates where many exotic phases have been discovered, such as: the charge-density-wave (CDW), spin-density-wave (SDW) and pair-density-wave (PDW) states . To identify these novel quantum phases is an important research direction in the coming decade.

Quantum phase transitions (QPTs), the phase transitions at zero temperature due to quantum fluctuations, result in many fascinating but poorly understood phenomena in condensed matter and cold atom systems. Unconventional metallic or strange metal (SM) states are generic features in strongly correlated electron systems in equilibrium close to QPTs, including high-Tc cuprate, Fe-based superconductors, and heavy-fermion metals and superconductors. These “strange” phenomena in electronic and thermodynamic observables include T-linear or T-sub-linear power-law resistivity at low temperatures, a power-law

singularity in spin susceptibility, a T-logarithmic specific heat coefficient. Due to the enhanced quantum fluctuations near quantum critical points (QCPs), a vanishing of the quasiparticle weight and divergence of the electron effective mass were observed. The quasiparticle picture within Landau’s Fermi liquid (LFL) framework breaks down, hence the SM state is a non-Fermi liquid. The mechanism of strange metal has become one of the outstanding open problems in correlated electron systems. Previous theoretical attempts have not been successful to account for these exotic behaviors. A new paradigm is urgently needed to account for these phenomena.

Due to the advances in experimental techniques, new surprising phenomena occur when systems close to out of equilibrium QPTs either by voltage bias (steady state non-equilibrium) or under a sudden quench (dynamical non-equilibrium). The former case can be realized in nano-devices (eg. a voltage biased quantum dot), while the latter has recently been realized in cold-atoms (Newton’s cradle setup is realized in one-dimensional Bose gases) and nano-devices (pump-probe spectroscopy). Important fundamental questions to be addressed include: for steady-state QPTs--what is the different role played by the voltage bias near nonequilibrium QCP from that for temperature near equilibrium QCP? Is there a fluctuation-dissipation theorem similar to that in equilibrium? What is the distinct scaling form of

observables from that in equilibrium? For quench QPTs--the time scales for thermalization, the possibility of pre-thermalized regime, quench dynamics near quantum phase transitions, and the existence of a generalized Gibbs ensemble (GGE) describing the steady state.

(3) Fractionalization, quantum spin liquids, and emergent gauge theories

Fractionalization is one of the emergent quantum phenomena in strongly correlated systems. The most well-known case is the one dimensional Luttinger liquids, where the electrons are fractionalized into spinon and holon. In two dimensions, more exotic entanglement patterns could be realized and leads to fractionalized quasiparticles, anyons, with non-trivial statistics. The study of such emergent phenomena is important for fundamental research and valuable for the developments of quantum technologies. One of the key ingredients to achieve such emergent quantum phenomena is the highly degenerated Hilbert space with non-trivial constraints. Frustrated quantum magnets are a suitable platform to study related

phenomena since the competition in energy leads to macroscopic degenerate configuration with non-trivial local constraints. Quantum fluctuations hybrid those degenerated states and lead to exotic fractionalization behavior. One important discovery for frustrated quantum magnets is the resonating valence bond (RVB) states proposed by P. W. Anderson in 1973. Any local order parameters vanish for the RVB state, suggesting such a quantum state of matter is beyond the Ginsburg-Landau paradigm. Such quantum states are highly entangled, to capture the non-local structure of entanglement, the low energy effective theory is closely related to the gauge theories. Besides, the gauge structure of the theory also

provides non-trivial kinetic constraints and leads to novel dynamical behavior.

The fundamental questions in the topic are (1) How do the gauge fields emerge from the microscopic models that link to the effective gauge theories? (2) What are the properties of these fractionalized systems that can be experimentally probed and can be theoretically understood? (3) Are there other models that go beyond the current gauge theory description? (4) Physics of real-time dynamics of lattice gauge theories are poorly understood, how to design numerical methods to explore the possible interesting phenomena? (5) Bridging numerical methods and theoretical properties to identify highly-entangled quantum matter in experiments.

We will also try to use machine learning (or AI) techniques here to search for exotic quantum

fractionalized spin liquid states in various quantum magnets.

**IV. Activities:**

*Regular monthly joint meeting/discussions within TG members

*Annual summer school and workshop (July 26-30, 2021)

*Symposium in annual meeting of Taiwan Physical Society

*International visitors

**V. Expected achievements:**

We expect to have breakthrough among the following topics:

(1) Correlation driven topological phases of matter and Majorana fermions

-- Interplay of electron correlation and topological properties in topological insulators, e.g. topological Mott insulators, topological Kondo insulators, topological Weyl Kondo insulators.

-- Search for exotic surface superconductivity properties, e.g. Majorana zero mode on the surface of spherical topological insulator

-- Propose new topological superconductors mediated by Kondo interactions

--New approaches to realize Majorana fermions in correlated electron systems on novel 2D materials, such as: in graphene-based and Transition metal dichalcogenide (TMD) materials with honeycomb structures,

--Search for Majorana spin liquid state in Kitaev related spin models.

--Majorana fermions in Kondo insulators

(2) Novel quantum phases, quantum phase transitions in and out of equilibrium

-Theory of pseudogap phase in cuprates as disordered PDW state

--Mechanism of superconductivity in hydrogen superconductors

--Equilibrium and non-equilibrium topological quantum phase transitions

--Non-equilibrium and dynamical quantum phase transitions

--Mechanism of strange metal state in unconventional superconductors (cuprates, heavy-fermion, twisted bi-layer graphene)

--Quantum quench in light-matter interacting cold atoms, cavity quantum electrodynamics, quantum impurity, and low-dimensional interacting systems

--Quench dynamics at topological phase transitions

(3) Fractionalization, quantum spin liquids, and emergent gauge theories

---theoretical properties such as entanglement measures of the spin-liquids and other fractionalizations

--experimentally probes of the spin-liquids and other fractionalizations

---exact solvable models

---construct microscopic models that host non-abelian anyons and fractons

---dynamics and constrained systems

**VI. Collaborations:**

Collaborations in Taiwan:

Chung-Yu Mou (NTHU), Ting-Kuo Lee (IoP, Academia Sinica), Di-Jing Huang (NSRRC, exp.)

Woei Wu Pai (NTU, exp.),

International Collaborations:

Eva Andrei (Rutgers U.), Alexei Tsvelik (Brookhaven Nat. Lab.), Harold Baranger (Duke U.),

Gleb Finkelstein (Duke U.), Natan Andrei (Rutgers U.)