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<html>
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<link rel="icon" href="icon.png" type="image/png">
<title>Research - Yi-Ting Tu (凃懿庭)</title>
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<body class="text-black bg-white">
<div class="d-flex h-5 text-center text-white bg-dark">
<div class="cover-container d-flex w-100 h-100 p-3 mx-auto flex-column">
<header class="mb-auto">
<div>
<h5 class="float-md-start mb-0 mt-1" style="color:rgba(255, 255, 255, .5)">Yi-Ting Tu</h3>
<nav class="nav nav-masthead justify-content-center float-md-end">
<a class="nav-link" href="https://yitingtu.com">Home</a>
<a class="nav-link" href="https://yitingtu.com/CV">CV</a>
<a class="nav-link active" aria-current="page" href="#">Research</a>
<a class="nav-link" href="https://yitingtu.com/programming">Programming</a>
</nav>
</div>
</header>
</div>
</div>
<div class="container border rounded mt-5">
<h4 class="text-center"> Synchronization in Many-body Localization (2025)</h4>
<div class="row">
<div class="col-md-6">
<center>
<img src="synchronization.svg" width="380">
</center>
</div>
<div class="col-md-6">
<p>
We found a coherently synchronized oscillation behavior of a many-body localized system with a mirror symmetry, where the synchronization transition is induced by interaction. We build a theory for this behavior using an effective Ising model, such that the synchronization transition is mapped to the ferromagnetic transition.
</p>
<p>Collaborator: Zi-Jian Li (李子健)<br>
Advisor: Sankar Das Sarma</p>
<div class="col-md-12">
<a href="https://arxiv.org/pdf/2512.11953.pdf" class="btn btn-primary mb-2">arXiv</a>
</div>
</div>
</div>
</div>
<div class="container border rounded mt-5">
<h4 class="text-center"> Anomalies of global symmetries on the lattice (2024–2025)</h4>
<div class="row">
<div class="col-md-6">
<center>
<object type="image/svg+xml" data="anomaly.svg" width="300"></object>
</center>
</div>
<div class="col-md-6">
<p>
We study the lattice counterpart of 't Hooft anomalies of global symmetries using quantum cellular automata (QCA). My contribution includes extracting cohomological invariants using both the symmetry restriction picture and the homotopy/domain wall picture, and exploring the consequences of the anomalies on symmetric commuting projector models. Conclusions in this part include the obstruction to having a trivial symmetric/symmetry broken many-body localized (MBL) phase, and the relationship between the anomaly class, the eigenstate topological order, the structure of its boundary algebra, and the quantum dimensions of the bulk symmetry defects.
</p>
<p>Collaborators: David M. Long, Dominic V. Else<br>
<div class="col-md-12">
[1] <a href="https://journals.aps.org/prx/abstract/10.1103/m188-w1ct" class="btn btn-primary mb-2">PRX</a>
<a href="https://arxiv.org/pdf/2507.21209.pdf" class="btn btn-primary mb-2">arXiv</a> (Main paper, with more results on this topic)<br>
[2] <a href="slides_anomaly.pdf" class="btn btn-success mb-2">Slides (APS March ’25)</a> (Application to Floquet time crystals)
</div>
</div>
</div>
</div>
<div class="container border rounded mt-5">
<h4 class="text-center"> Many-body Localization in a Slowly Varying Potential (2025)</h4>
<div class="row">
<div class="col-md-6">
<center>
<img src="slowlyvarying.jpg" width="350">
</center>
</div>
<div class="col-md-6">
<p>
We numerically study the properties of an interacting model with a potential which varies slower and slower as
one goes further away from the origin, showing that it has finite-size MBL behavior and effective criticality.
</p>
<p>Collaborator: Zi-Jian Li (李子健)<br>
Advisor: Sankar Das Sarma</p>
<div class="col-md-12">
<a href="https://journals.aps.org/prb/abstract/10.1103/v988-qdsx" class="btn btn-primary mb-2">PRB</a>
<a href="https://arxiv.org/pdf/2503.22096.pdf" class="btn btn-primary mb-2">arXiv</a>
</div>
</div>
</div>
</div>
</div>
<div class="container border rounded mt-5">
<div class="container border rounded mt-5">
<h4 class="text-center"> Non-ergodic extended behavior in the prethermal regime (2024)</h4>
<div class="row">
<div class="col-md-6">
<center>
<object type="image/svg+xml" data="prethermal.svg" width="300"></object>
</center>
</div>
<div class="col-md-6">
<p>
We study the dynamics of various disordered spin chains in the prethermal regime, concluding that the
previously-observed non-ergodic extended behavior is not related to quasiperiodicity or the mobility edge,
but can be perturbatively explained for any potential with regularly spaced deep wells.
</p>
<p>Collaborator: David M. Long<br>
Advisor: Sankar Das Sarma</p>
<div class="col-md-12">
<a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.109.214309"
class="btn btn-primary mb-2">PRB</a>
<a href="https://arxiv.org/pdf/2405.01622.pdf" class="btn btn-primary mb-2">arXiv</a>
</div>
</div>
</div>
</div>
</div>
<div class="container border rounded mt-5">
<h4 class="text-center"> Properties of metallic resistivity due to phonon scattering (2024)</h4>
<div class="row">
<div class="col-md-6">
<center>
<object type="image/svg+xml" data="phonon.svg" width="300"></object>
</center>
</div>
<div class="col-md-6">
<p>
We discuss the linear-in-temperature electronic resistivity due to the scattering by many random phonon modes
and the difference between the "apparent asymptote" and the true asymptote, which may have consequences on the
interpretation of some recent experiments.
</p>
<p>Advisor: Sankar Das Sarma</p>
<div class="col-md-12">
[1]
<a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.109.235118"
class="btn btn-primary mb-2">PRB</a>
<a href="https://arxiv.org/pdf/2403.09890.pdf" class="btn btn-primary mb-2">arXiv</a> (Many phonon modes)
</div>
<div class="col-md-12">
[2]
<a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.110.075151"
class="btn btn-primary mb-2">PRB</a>
<a href="https://arxiv.org/pdf/2407.01664.pdf" class="btn btn-primary mb-2">arXiv</a> (Apparent asymptote)
</div>
</div>
</div>
</div>
</div>
<div class="container border rounded mt-5">
<h4 class="text-center"> Stability of exciton phase in a 2D bilayer system (2024)</h4>
<div class="row">
<div class="col-md-6">
<center>
<object type="image/svg+xml" data="exciton.svg" width="300"></object>
</center>
</div>
<div class="col-md-6">
<p>
We compare the ground state energy of a 2D bilayer electron-hole system assuming that it is an electron-hole
plasma and that it is an exciton gas under various screening assumptions, from which the statbility of the
exciton phase can be estimated.
</p>
<p>Collaborator: Seth M. Davis<br>
Advisor: Sankar Das Sarma</p>
<div class="col-md-12">
<a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.109.165307"
class="btn btn-primary mb-2">PRB</a>
<a href="https://arxiv.org/pdf/2402.00866.pdf" class="btn btn-primary mb-2">arXiv</a>
</div>
</div>
</div>
</div>
</div>
<div class="container border rounded mt-5">
<h4 class="text-center"> Energy-dependent Many-body localization (2023)</h4>
<div class="row">
<div class="col-md-6">
<center>
<object type="image/svg+xml" data="GAA.svg" width="300"></object>
</center>
</div>
<div class="col-md-6">
<p>
We simulate a clean spin chain (thermal bath) coupled to an interacting quasiperiodic spin chain with a
mobility edge, with the latter initialized in an energy eigenstate, and using the long-time evolution of the
system to extract three behaviors: ETH, non-ergodic extended, and localized.
</p>
<p>Collaborator: DinhDuy Vu (Vũ Trần Đình Duy)<br>
Advisor: Sankar Das Sarma</p>
<div class="col-md-12">
<a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.108.064313"
class="btn btn-primary mb-2">PRB</a>
<a href="https://arxiv.org/pdf/2305.15471.pdf" class="btn btn-primary mb-2">arXiv</a>
<a href="slides_GAA.pdf" class="btn btn-success mb-2">Slides (APS March ’24)</a>
</div>
</div>
</div>
</div>
</div>
<div class="container border rounded mt-5">
<h4 class="text-center"> Wiedemann-Franz law in graphene (2022–2023)</h4>
<div class="row">
<div class="col-md-6">
<center>
<object type="image/svg+xml" data="graphene.svg" width="300"></object>
</center>
</div>
<div class="col-md-6">
<div class="col-md-12">
<p>
We calculate the Lorenz ratio of graphene with a bipolar diffusive Boltzmann transport theory with disorders
and phonon scattering, which provides an alternative explanation for the sharp finite-temperature peak of
the Lorenz ratio observed in an experimental paper.
</p>
<p>Advisor: Sankar Das Sarma</p>
<div class="col-md-12">
[1]
<a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.107.085401"
class="btn btn-primary mb-2">PRB</a>
<a href="https://arxiv.org/pdf/2211.05192.pdf" class="btn btn-primary mb-2">arXiv</a> (Basic calculations)
</div>
<div class="col-md-12">
[2]
<a href="https://link.aps.org/doi/10.1103/PhysRevB.108.245415" class="btn btn-primary mb-2">PRB</a>
<a href="https://arxiv.org/pdf/2307.05477.pdf" class="btn btn-primary mb-2">arXiv</a> (With magnetic
field/bilayer graphene)
</div>
</div>
</div>
</div>
</div>
<div class="container border rounded mt-5">
<h4 class="text-center"> Many body localization in quasiperiodic systems (2022)</h4>
<div class="row">
<div class="col-md-6">
<center>
<object type="image/svg+xml" data="avalanche.svg" width="300"></object>
</center>
</div>
<div class="col-md-6">
<div class="col-md-12">
<p>
We study the avalanche instability of a quasiperiodic spin chain. My contribution involves calculating the decay rate of bath-coupled small chains numerically to simulate thermal propagation in a large quasiperiodic MBL systems.
</p>
<p>Collaborator: DinhDuy Vu (Vũ Trần Đình Duy)<br>
Advisor: Sankar Das Sarma</p>
<div class="col-md-12">
<a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.107.014203"
class="btn btn-primary mb-2">PRB</a>
<a href="https://arxiv.org/pdf/2207.05051.pdf" class="btn btn-primary mb-2">arXiv</a>
<a href="slides_avalanche.pdf" class="btn btn-success mb-2">Slides (APS March ’23)</a>
</div>
</div>
</div>
</div>
</div>
<div class="container border rounded mt-5">
<h4 class="text-center">Fidelity in Non-Hermitian quantum systems (2022)</h4>
<div class="row">
<div class="col-md-6">
<center>
<object type="image/svg+xml" data="fidelity.svg" width="250"></object>
</center>
</div>
<div class="col-md-6">
<div class="col-md-12">
<p> We consider the properties of the fidelity and fidelity susceptibility in non-Hermitian quantum systems
with parity-time symmetry, and its application in numerics to detect quantum phase transitions. My contribution is mainly in the application to the SSH and generalized SSH models.
</p>
<p>Collaborators: Iksu Jang (장익수), Po-Yao Chang (張博堯), Yu-Chin Tzeng (曾郁欽)</p>
<div class="col-md-12">
<a href="https://quantum-journal.org/papers/q-2023-03-23-960/" class="btn btn-primary mb-2">Quantum</a>
<a href="https://arxiv.org/pdf/2203.01834.pdf" class="btn btn-primary mb-2">arXiv</a>
</div>
</div>
</div>
</div>
</div>
<div class="container border rounded mt-5">
<h4 class="text-center">Non-Hermitian many-body entanglement (2021)</h4>
<div class="row">
<div class="col-md-6">
<center>
<object type="image/svg+xml" data="nonhermitian.svg" width="350"></object>
</center>
</div>
<div class="col-md-6">
<div class="col-md-12">
<p>We generalize the entanglement entropy to non-Hermitian quantum systems such that the scaling properties of
conformal field theories are retained at critical points. My contribution is in the theoretical formalism and the numerical confirmation for the SSH and generalized SSH models.</p>
<p>Collaborators: Yu-Chin Tzeng (曾郁欽), Po-Yao Chang (張博堯)</p>
<div class="col-md-12">
<a href="https://scipost.org/SciPostPhys.12.6.194" class="btn btn-primary mb-2">SciPostPhys</a>
<a href="https://arxiv.org/pdf/2107.13006.pdf" class="btn btn-primary mb-2">arXiv</a>
</div>
</div>
</div>
</div>
</div>
<div class="container border rounded mt-5">
<h4 class="text-center">Construction of non-Abelian fractons (2021)</h4>
<div class="row">
<div class="col-md-6">
<center>
<object type="image/svg+xml" data="fracton.svg" width="350"></object>
</center>
</div>
<div class="col-md-6">
<div class="col-md-12">
<p>We develop a generalized version of the gauging procedure, and use it to construct non-Abelian fractons and
explore their algebraic properties.</p>
<p>Advisor: Po-Yao Chang (張博堯)</p>
<div class="card mb-2">
<button class="btn card-header" id="headingOne" data-bs-toggle="collapse" data-bs-target="#summaryFracton"
aria-expanded="true" aria-controls="summaryFracton">
Popular Summary
</button>
<div class="collapse" id="summaryFracton">
<div class="card card-body">
<p>Non-Abelian anyons are the quasiparticles with fascinating properties in two-dimensional topological
phases of matter, which are candidates for fault-tolerant quantum computation. Beyond the traditional
type of topological phases, fracton orders in three dimensions have the unique feature that some
excitations are immobile, making them suitable for quantum memories. Non-Abelian fractons combine the
two features above, and are important subjects for theoretical developments and potential applications
to quantum information science. However, due to lack of a generic mathematical description of the
non-Abelian fractions, a systematical construction of the lattice model is desired. Here, we develop a
novel way to construct non-Abelian fractons on lattices based on the gauging principle.</p>
<p>The principle of gauging has a tremendous success in obtaining several topological phases of matters.
In electromagnetism, one can start from the symmetry of a matter field, construct the gauge potentials
and the gauge transformation, and finally obtain the properties of the electric charge and the
magnetic flux. Now, we generalize the construction by starting from a matter field having exotic
symmetries, and find that the resulting “electric charges” and “magnetic fluxes” contain non-Abelian
fractons. Moreover, we find that, under certain conditions, the algebraic properties of those charges
and fluxes are the same as their counterparts in two-dimensional lattice gauge theory for non-Abelian
anyons.</p>
<p>Our construction using the gauging principle makes the identification of species and properties of
fractons more straightforward. In particular, the correspondence between fractons and anyons from the
algebtric structure sheds light on classifying fracton orders.</p>
</div>
</div>
</div>
<div class="col-md-12">
<a href="https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.043084"
class="btn btn-primary mb-2">PRResearch</a>
<a href="https://arxiv.org/pdf/2103.08603.pdf" class="btn btn-primary mb-2">arXiv</a>
<a href="slides_fracton.pdf" class="btn btn-success mb-2">Slides (NCTS workshop)</a>
</div>
</div>
</div>
</div>
</div>
<div class="container border rounded mt-5 mb-5">
<h4 class="text-center">Quantum entanglement and Symplectic geometry (2019)</h4>
<div class="row">
<div class="col-md-6">
<center>
<object type="image/svg+xml" data="symplectic.svg" width="350"></object>
</center>
</div>
<div class="col-md-6">
<div class="col-md-12">
<p>We use the mathematical language of symplectic geometry to reformulate the positive partial transpose
criterion in phase space.</p>
<p>Advisor: Ray-Kuang Lee (李瑞光)</p>
<div class="col-md-12">
<a href="poster_symplectic.pdf" class="btn btn-success mb-2">Poster (AQIS’18)</a>
<a href="slides_symplectic.pdf" class="btn btn-success mb-2">Slides (YRFQIS’19)</a>
</div>
</body>
</html>