Jinmin Yi - Academia.edu (original) (raw)

Papers by Jinmin Yi

Research paper thumbnail of Lieb-Schultz-Mattis theorems and generalizations in long-range interacting systems

arXiv (Cornell University), May 23, 2024

In a unified fashion, we establish Lieb-Schultz-Mattis (LSM) theorems and their generalizations i... more In a unified fashion, we establish Lieb-Schultz-Mattis (LSM) theorems and their generalizations in systems with long-range interactions. We show that, for a quantum spin chain, if the interactions decay fast enough as their ranges increase and the Hamiltonian has an anomalous symmetry, the Hamiltonian cannot have a unique gapped symmetric ground state. If the Hamiltonian contains only 2-spin interactions, these theorems hold when the interactions decay faster than 1/r 2 , with r the distance between the two interacting spins. Moreover, any pure state with an anomalous symmetry, which may not be a ground state of any natural Hamiltonian, must be long-range entangled. The symmetries we consider include on-site internal symmetries combined with lattice translation symmetries, and they can also extend to purely internal but non-on-site symmetries. Moreover, these internal symmetries can be discrete or continuous. We explore the applications of the theorems through various examples.

Research paper thumbnail of Absence of localization in Weyl semimetals

arXiv (Cornell University), Feb 21, 2024

Research paper thumbnail of Complexity and order in approximate quantum error-correcting codes

arXiv (Cornell University), Oct 6, 2023

Research paper thumbnail of Topological order in interacting semimetals

arXiv (Cornell University), Jan 9, 2023

It has recently been demonstrated that it is possible to open a gap in a magnetic Weyl semimetal,... more It has recently been demonstrated that it is possible to open a gap in a magnetic Weyl semimetal, while preserving the chiral anomaly along with the charge conservation and translational symmetries, which all protect the gapless nodes in a weakly interacting semimetal. The resulting state was shown to be a nontrivial generalization of a nonabelian fractional quantum Hall liquid to three dimensions. Here we point out that a second fractional quantum Hall state exists in this case. This state has exactly the same electrical and thermal Hall responses as the first, but a distinct (fracton) topological order. Moreover, the existence of this second fractional quantum Hall state necessarily implies a gapless phase, which has identical topological response to a noninteracting Weyl semimetal, but is distinct from it. This may be viewed as a generalization (in a weaker form) of the known duality between a noninteracting two-dimensional Dirac fermion and QED3 to 3 + 1 dimensions. In addition we discuss a (3 + 1)-dimensional topologically ordered state, obtained by gapping a nodal line semimetal without breaking symmetries.

Research paper thumbnail of Deep Learning for Topological Invariants

ArXiv, 2018

Ning Sun, ∗ Jinmin Yi, 2, ∗ Pengfei Zhang, Huitao Shen, and Hui Zhai 4 Institute for Advanced Stu... more Ning Sun, ∗ Jinmin Yi, 2, ∗ Pengfei Zhang, Huitao Shen, and Hui Zhai 4 Institute for Advanced Study, Tsinghua University, Beijing, 100084, China Department of Physics, Peking University, Beijing, 100871, China Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Collaborative Innovation Center of Quantum Matter, Beijing, 100084, China (Dated: May 29, 2018)

Research paper thumbnail of Deep learning topological invariants of band insulators

Physical Review B, 2018

In this work we design and train deep neural networks to predict topological invariants for one-d... more In this work we design and train deep neural networks to predict topological invariants for one-dimensional four-band insulators in AIII class whose topological invariant is the winding number, and two-dimensional two-band insulators in A class whose topological invariant is the Chern number. Given Hamiltonians in the momentum space as the input, neural networks can predict topological invariants for both classes with accuracy close to or higher than 90%, even for Hamiltonians whose invariants are beyond the training data set. Despite the complexity of the neural network, we find that the output of certain intermediate hidden layers resembles either the winding angle for models in AIII class or the solid angle (Berry curvature) for models in A class, indicating that neural networks essentially capture the mathematical formula of topological invariants. Our work demonstrates the ability of neural networks to predict topological invariants for complicated models with local Hamiltonians as the only input, and offers an example that even a deep neural network is understandable.

Research paper thumbnail of Topological order in interacting semimetals

Physical Review B

It has recently been demonstrated that it is possible to open a gap in a magnetic Weyl semimetal,... more It has recently been demonstrated that it is possible to open a gap in a magnetic Weyl semimetal, while preserving the chiral anomaly along with the charge conservation and translational symmetries, which all protect the gapless nodes in a weakly interacting semimetal. The resulting state was shown to be a nontrivial generalization of a non-Abelian fractional quantum Hall liquid to three dimensions. Here we point out that a second fractional quantum Hall state exists in this case. This state has exactly the same electrical and thermal Hall responses as the first, but a distinct (fracton) topological order. Moreover, the existence of this second fractional quantum Hall state necessarily implies a gapless phase, which has identical topological response to a noninteracting Weyl semimetal, but is distinct from it. This may be viewed as a generalization (in a weaker form) of the known duality between a noninteracting two-dimensional Dirac fermion and QED 3 to 3 + 1 dimensions. In addition we discuss a (3 + 1)-dimensional topologically ordered state, obtained by gapping a nodal line semimetal without breaking symmetries.

Research paper thumbnail of Lieb-Schultz-Mattis theorems and generalizations in long-range interacting systems

arXiv (Cornell University), May 23, 2024

In a unified fashion, we establish Lieb-Schultz-Mattis (LSM) theorems and their generalizations i... more In a unified fashion, we establish Lieb-Schultz-Mattis (LSM) theorems and their generalizations in systems with long-range interactions. We show that, for a quantum spin chain, if the interactions decay fast enough as their ranges increase and the Hamiltonian has an anomalous symmetry, the Hamiltonian cannot have a unique gapped symmetric ground state. If the Hamiltonian contains only 2-spin interactions, these theorems hold when the interactions decay faster than 1/r 2 , with r the distance between the two interacting spins. Moreover, any pure state with an anomalous symmetry, which may not be a ground state of any natural Hamiltonian, must be long-range entangled. The symmetries we consider include on-site internal symmetries combined with lattice translation symmetries, and they can also extend to purely internal but non-on-site symmetries. Moreover, these internal symmetries can be discrete or continuous. We explore the applications of the theorems through various examples.

Research paper thumbnail of Absence of localization in Weyl semimetals

arXiv (Cornell University), Feb 21, 2024

Research paper thumbnail of Complexity and order in approximate quantum error-correcting codes

arXiv (Cornell University), Oct 6, 2023

Research paper thumbnail of Topological order in interacting semimetals

arXiv (Cornell University), Jan 9, 2023

It has recently been demonstrated that it is possible to open a gap in a magnetic Weyl semimetal,... more It has recently been demonstrated that it is possible to open a gap in a magnetic Weyl semimetal, while preserving the chiral anomaly along with the charge conservation and translational symmetries, which all protect the gapless nodes in a weakly interacting semimetal. The resulting state was shown to be a nontrivial generalization of a nonabelian fractional quantum Hall liquid to three dimensions. Here we point out that a second fractional quantum Hall state exists in this case. This state has exactly the same electrical and thermal Hall responses as the first, but a distinct (fracton) topological order. Moreover, the existence of this second fractional quantum Hall state necessarily implies a gapless phase, which has identical topological response to a noninteracting Weyl semimetal, but is distinct from it. This may be viewed as a generalization (in a weaker form) of the known duality between a noninteracting two-dimensional Dirac fermion and QED3 to 3 + 1 dimensions. In addition we discuss a (3 + 1)-dimensional topologically ordered state, obtained by gapping a nodal line semimetal without breaking symmetries.

Research paper thumbnail of Deep Learning for Topological Invariants

ArXiv, 2018

Ning Sun, ∗ Jinmin Yi, 2, ∗ Pengfei Zhang, Huitao Shen, and Hui Zhai 4 Institute for Advanced Stu... more Ning Sun, ∗ Jinmin Yi, 2, ∗ Pengfei Zhang, Huitao Shen, and Hui Zhai 4 Institute for Advanced Study, Tsinghua University, Beijing, 100084, China Department of Physics, Peking University, Beijing, 100871, China Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Collaborative Innovation Center of Quantum Matter, Beijing, 100084, China (Dated: May 29, 2018)

Research paper thumbnail of Deep learning topological invariants of band insulators

Physical Review B, 2018

In this work we design and train deep neural networks to predict topological invariants for one-d... more In this work we design and train deep neural networks to predict topological invariants for one-dimensional four-band insulators in AIII class whose topological invariant is the winding number, and two-dimensional two-band insulators in A class whose topological invariant is the Chern number. Given Hamiltonians in the momentum space as the input, neural networks can predict topological invariants for both classes with accuracy close to or higher than 90%, even for Hamiltonians whose invariants are beyond the training data set. Despite the complexity of the neural network, we find that the output of certain intermediate hidden layers resembles either the winding angle for models in AIII class or the solid angle (Berry curvature) for models in A class, indicating that neural networks essentially capture the mathematical formula of topological invariants. Our work demonstrates the ability of neural networks to predict topological invariants for complicated models with local Hamiltonians as the only input, and offers an example that even a deep neural network is understandable.

Research paper thumbnail of Topological order in interacting semimetals

Physical Review B

It has recently been demonstrated that it is possible to open a gap in a magnetic Weyl semimetal,... more It has recently been demonstrated that it is possible to open a gap in a magnetic Weyl semimetal, while preserving the chiral anomaly along with the charge conservation and translational symmetries, which all protect the gapless nodes in a weakly interacting semimetal. The resulting state was shown to be a nontrivial generalization of a non-Abelian fractional quantum Hall liquid to three dimensions. Here we point out that a second fractional quantum Hall state exists in this case. This state has exactly the same electrical and thermal Hall responses as the first, but a distinct (fracton) topological order. Moreover, the existence of this second fractional quantum Hall state necessarily implies a gapless phase, which has identical topological response to a noninteracting Weyl semimetal, but is distinct from it. This may be viewed as a generalization (in a weaker form) of the known duality between a noninteracting two-dimensional Dirac fermion and QED 3 to 3 + 1 dimensions. In addition we discuss a (3 + 1)-dimensional topologically ordered state, obtained by gapping a nodal line semimetal without breaking symmetries.