physics journal club – Jiaqi Cai's Homepage

This journal club aims to explore a diverse range of topics within the fields of condensed matter physics, high-energy physics, mathematical physics, instrumentation, and metrology.

Biweekly, I will select a topic and provide an extensive compilation of key references to the best of my knowledge. Following our discussions, I encourage all participants to share their notes and slides on the subject. Moreover, I highly encourage utilizing the provided contents for further individual discussions. Fascinating notes and slides will also be shared within the group platform. Some topics will be discussed again.

Topic. 11 Deconfined quantum critical point

Refernces:

Comment:

Topic. 10 Quantum Fuzziness and Hall effct
References:
arXiv:hep-th/0407007 (2004)
Phys. Rev. Lett. 51, 605 (1983)
Phys. Rev. X 13, 021009 (2023), arXiv: 2306.04681 (2023), arXiv:2306.16435 (2023)
https://dataspace.princeton.edu/handle/88435/dsp01n009w241h
https://podcasts.ox.ac.uk/quantum-geometry-exclusion-statistics-and-geometry- flux-attachment-2d-landau-levels

Comment: E. Schrödinger has proposed a wavefunction $\psi(\bf{x}, t)$ or $\psi(\bf{x}, E)$ where $\bf{x}, \bf{p} \in R^3$ and $t,E\in R$ to formulate quantum mechanics, i.e., wavefunction on a classical Euclidean geometry. Here, the coordinate can be treated as the eigenvalue of the position/momentum operator $\hat{x}, \hat{p}$ . Key discovery of canonical quantization is that as an operator $[\hat{x},\hat{p}]=i$ , i.e., the commutators of operator are nontrivial. However, can we impose a nontrivial commutator to position/momentum coordinates, that is, $[x_i,x_j] \ne 0$ and completely discard classical geometry? In this way, a non-commutative algebra is attached to the space-time coordinates. This idea souns like Kaluza-Klein’s generalization of 3+1D field theory to 5D to unify gravitational theory and electromagnetic theory. The key idea is to glue an additional structure to the spacetime coordinates.
In the recommended journal club, we will find the necessity of including this non-commutative algebra in the condensed matter universe from the insights of quantum Hall effect and Hofstadter butterfly spectrum. Haldane constructed so-called Haldane potential which is the basis for many electron problem in the fuzzy-2 sphere, and pointed out this fuzziness in the quantum Hall effect can be the key to construct new topological phases. Very recently, the quantized version of Haldane fuzzy sphere is found to be an efficient tool to explore phase transitions and associated conformal field theory.
Let’s try to make the physics a bit more transparent. Consider a non-interacting electron’s Hamiltonian without magnetic field in two dimension: $H = \int d\mathbf{k} \psi_\mathbf{k}^\dagger (H(\mathbf{k})-\mu) \psi_\mathbf{k}$ , we know that the spectrum of the system is given by diagonalizing $H(\bf{k})$ in a local $\bf{k}$ point. Now we turn on magnetic field, Hofstadter/Peierls substitution taught us, to simulate such a system, now you do the transformation: $k_x+i k_y \rightarrow k_{0 x}+i k_{0 y}+\sqrt{2} \ell_B^{-1} a, \quad k_x-i k_y \rightarrow k_{0 x}-i k_{0 y}+\sqrt{2} \ell_B^{-1} a^{\dagger}$ , where $[a,a^\dagger]=1$ is boson harmonic operators’ commutator and $\bf{k}_0$ is the residual vector from a guiding center. By cutting $a$ to be $N$ th order materix form $\sqrt n \delta_{n,n-1}$ and diagonalizing $H_{\mathbf{k_0}}(a^\dagger, a)$ you can get the excitation spectrum in a finite magnetic field $B = \Phi_0/\ell_B^2$ , the so called Hofstadter spectrum. Now, let me ask you a question, which `local` point you are at for constructing the Hamiltonian matrix numerically? You will find that you are `fuzzy` now — the local point is no longer a momentum but an algebra with nontrivial structure (we should admit that harmonic oscillator is never a trivial object) with the `coordinates` $z = k_x+ik_y, [z,z*]=2/\ell _B^2$ .

Topic. 9 Dark matter detection: RF to ultraviolet (June. 12)
Refrences:
Wiki: https://en.m.wikipedia.org/wiki/Axion_Dark_Matter_Experiment
UW ADMX: https://depts.washington.edu/admx/
Bartram, Chelsea, et al. “Axion dark matter experiment: Run 1B analysis details.” Physical Review D 103.3 (2021): 032002.
Lehnert, Konrad. “Quantum enhanced metrology in the search for fundamental physical phenomena.” SciPost Physics Lecture Notes (2022): 040.
Wurtz, K., et al. “Cavity entanglement and state swapping to accelerate the search for axion dark matter.” PRX Quantum 2.4 (2021): 040350.
Backes, Kelly M., et al. “A quantum enhanced search for dark matter axions.” Nature 590.7845 (2021): 238-242.
Palken, D. A., et al. “Improved analysis framework for axion dark matter searches.” Physical Review D 101.12 (2020): 123011.
Bothwell, Tobias, et al. “Resolving the gravitational redshift across a millimetre-scale atomic sample.” Nature 602.7897 (2022): 420-424.
Roussy, Tanya S., et al. “Experimental constraint on axionlike particles over seven orders of magnitude in mass.” Physical Review Letters 126.17 (2021): 171301.
Antypas, D., et al. “New horizons: scalar and vector ultralight dark matter.” arXiv preprint arXiv:2203.14915 (2022).
Fujimoto, Hiroki, et al. “Dark matter Axion search with riNg Cavity Experiment DANCE: Design and development of auxiliary cavity for simultaneous resonance of linear polarizations.” Journal of Physics: Conference Series. Vol. 2156. No. 1. IOP Publishing, 2021.

Comment:

The advances in quantum technologies have opened up exciting possibilities for the new era of quantum metrology. Quantum technologies, ranging from superconducting circuits, cavity systems, nanomechanics, atomic clocks, ultracold atomic arrays, and 2D materials (e.g., quantum Hall effect), have already demonstrated significant achievements in the realm of precision measurements. The revision of SI units to be based on fundamental constants is a clear indication of the development of a quantum SI, where quantum technologies can play a crucial role in providing precise measurements and serving as potential quantum standards.

However, the ultimate goal and Holy Grail of precise measurement and quantum metrology lie in the discovery and comprehension of axion particles. Axions are hypothetical elementary particles that have been proposed as a solution to certain problems in particle physics and cosmology. Detecting and understanding axions could have transformative implications for both technology and our understanding of the universe.

Advancements in experimental techniques and sensitivity have brought us closer to the possibility of detecting axion particles. Although they are elusive and challenging to observe directly, various experimental efforts are underway to detect their presence indirectly through their hypothetical interactions with electromagnetic fields. The successful discovery of axions would not only open up new technological possibilities but also provide deep insights into the fundamental nature of our universe.

Topic. 8 Parton theory in high energy physics and condensed matter (Apr. 17)
Refrences:
Jain, Jainendra K. “Incompressible quantum Hall states.” Physical Review B 40.11 (1989): 8079.
Jain, Jainendra K. “Composite-fermion approach for the fractional quantum Hall effect.” Physical review letters 63.2 (1989): 199.
Wiki: https://en.wikipedia.org/wiki/Parton_(particle_physics)#:~:text=In%20particle%20physics%2C%20the%20parton,in%20high%2Denergy%20particle%20collisions
Feynman’s parton picutre: http://www2.physics.umd.edu/~yskim/feynman/partons.html

Comment: I fail to fully understand this topic. I understand the story for FQH. I admit the slave particles approach is very interesting. But how to connect the one used in high energy physics and condensed matter? Can I call all slave particles to be parton construction? What’s new we can learn from it?

Topic. 7 Grand Unification Theory(GUT) and anti-GUT (Apr. 17)
Refrences: preface chapter for Volovik’s textbook “The universe in a Helium droplet”.

Topic. 6 The Nagaoka-Thouless Ferromagnetism (Apr. 10)

References:
Tasaki, Hal. “From Nagaoka’s ferromagnetism to flat-band ferromagnetism and beyond: an introduction to ferromagnetism in the Hubbard model.” Progress of theoretical physics 99.4 (1998): 489-548.
Thouless, D. J. “Exchange in solid 3He and the Heisenberg Hamiltonian.” Proceedings of the Physical Society 86.5 (1965): 893.
Nagaoka, Yosuke. “Ferromagnetism in a narrow, almost half-filled s band.” Physical Review 147.1 (1966): 392.
Zhao, Wenjin, et al. “Gate-tunable heavy fermions in a moiré Kondo lattice.” Nature 616.7955 (2023): 61-65.
Anderson, Eric, et al. “Programming correlated magnetic states with gate-controlled moiré geometry.” Science (2023): eadg4268.
Xu, Muqing, et al. “Doping a frustrated Fermi-Hubbard magnet.” arXiv preprint arXiv:2212.13983 (2022).

Comment:

Quantum magnetism is an enthralling subject that continually captivates condensed matter physicists. Understanding how ferromagnetism emerges from interactions is a fundamental question in this field. While Hund’s rule (exchange interaction) can explain ferromagnetism in a ferromagnetic insulator, it falls short in explaining itinerant ferromagnets, specifically ferromagnetic metals. As a result, a plethora of alternative theories has been proposed, creating a fascinating zoology of ideas.

One such theory is Nagaoka ferromagnetism, which sheds light on how a single electron can induce a transition from the antiferromagnetic ground state of a Mott insulator on a specific lattice to a ferromagnetic state. Interestingly, this electron remains mobile, and the mechanism has been employed to explain recent experiments involving doping frustrated antiferromagnetic states. To gain a deeper understanding, I highly recommend delving into the technical details and exploring the connection to the topics discussed previously in the work presented by Junkai in the link provided: https://junkaidong.github.io/physics/ferromagnetism/.

Note:
https://junkaidong.github.io/physics/ferromagnetism/. Junkai is now a graduate student in Ashvin’s group at Harvard.

Topic. 5 The important role of Z2 symmetry in the Fermi liquid (Apr. 03)

References:
Anderson, Philip W., and F. Duncan M. Haldane. “The symmetries of fermion fluids at low dimensions.” Journal of Statistical Physics 103 (2001): 425-428.
Phillips, Philip W., Luke Yeo, and Edwin W. Huang. “Exact theory for superconductivity in a doped Mott insulator.” Nature Physics 16.12 (2020): 1175-1180.
Huang, Edwin W., Gabriele La Nave, and Philip W. Phillips. “Discrete symmetry breaking defines the Mott quartic fixed point.” Nature Physics 18.5 (2022): 511-516.

Comment:
The symmetry of a Fermi liquid may appear straightforward at first, with $SU(2)$ symmetry for spin and particle-hole pseudo-spin (Nambu description), leading to the natural assumption of a fundamental symmetry of $SU(2)\times SU(2)$ . However, Anderson and Haldane made a remarkable realization that the full symmetry of a free Fermionic model involves at least three $Z_2$ symmetries, as seen in Altland’s tenfold classification. The complete spinor of a free Fermionic model is described by four real Majorana operators, forming the full symmetry $O(4)$ , which is higher than $SU(2)\times SU(2)$ : $O(4)/Z_2 \simeq SU(2) \times SU(2)$ .

An important observation is that the Fermi-Hubbard interaction maximally violates the $Z_2$ symmetry. Despite this, Landau’s Fermi liquid theory showed that in 3D, a Fermi liquid can still be the ground state in a weakly interacting model. This led Anderson and Haldane to conclude that the extra symmetry is “picked up,” implying that the Fermi liquid actually represents a critical point of the interacting model. Unfortunately, this viewpoint was initially overlooked.

With the rise of quantum simulation and advancements in controlling hardcore bosons in superconducting qubits, there is now a realization that this $Z_2$ symmetry also classifies bosons and fermions, at least in 3D. In the absence of interactions, and with the full $Z_2$ symmetry present in the model, the Fermi liquid can be efficiently simulated using classical particles and hardcore bosons. However, when interactions that violate the $Z_2$ symmetry are introduced, a clear distinction between bosonic and fermionic behavior emerges, giving rise to quantum effects. This insight provides a compelling rationale for referring to such materials as “quantum materials.”

In this context, Philip Phillips’ work has significantly contributed to understanding interacting systems through the construction of toy models, such as the H-K model. The interplay of topology and short-range interaction-induced states like the fractional quantum Hall effect (FQH) remains a fascinating subject. Integrating these ideas into Philip’s framework for cuprates raises questions about the role of topology, the significance of short-range interactions, and how these factors fit together in the broader picture of quantum materials and their behavior. This integration of ideas can potentially shed light on the complex physics observed in cuprates and related materials.

Topic. 4 Feshbach and shape resonances (Mar. 20)

References:
Chin, Cheng, et al. “Feshbach resonances in ultracold gases.” Reviews of Modern Physics 82.2 (2010): 1225.
Feshbach, Herman. “A unified theory of nuclear reactions. II.” Annals of Physics 19.2 (1962): 287-313.
Fano, Ugo. “Effects of configuration interaction on intensities and phase shifts.” Physical review 124.6 (1961): 1866.
Schwartz, Ido, et al. “Electrically tunable feshbach resonances in twisted bilayer semiconductors.” Science 374.6565 (2021): 336-340.
Kuhlenkamp, Clemens, et al. “Tunable Feshbach resonances and their spectral signatures in bilayer semiconductors.” Physical Review Letters 129.3 (2022): 037401.
Takemura, Naotomo, et al. “Polaritonic feshbach resonance.” Nature Physics 10.7 (2014): 500-504.
Bryant, H. C., et al. “Observation of resonances near 11 eV in the photodetachment cross section of the H− ion.” Physical Review Letters 38.5 (1977): 228.
Broad, John T., and William P. Reinhardt. “One-and two-electron photoejection from H−: A multichannel J-matrix calculation.” Physical Review A 14.6 (1976): 2159.

Comment:
The concept of shape resonance exemplifies the remarkable success of Schrödinger’s single-particle quantum mechanics. This phenomenon arises from the overlapping regions of wavefunctions in different parameter spaces, combined with the quantum tunneling of possible states. Shape resonance plays a pivotal role in understanding and describing quantum mechanical interactions. On the other hand, Feshbach resonances, discovered by Feshbach, are many-body but semi-classical effects where a particle can temporarily bind with another system or particle and subsequently dissociate, significantly influencing the final state of the system compared to its initial state. A classic example of this effect is the autoionization of a helium ion, which can be modeled as the simplest example, and the scattering of a dimer molecule on a platinum surface. These resonances have profound implications and find crucial applications in various technical domains, particularly in controlling interactions in ultracold atom systems.

Topic. 3 Quantum geometry on superfluid weight, fractional Chern insulators and localization (Feb. 27)

References:
Kohn, Walter. “Theory of the insulating state.” Physical review 133.1A (1964): A171.
Herzog-Arbeitman, Jonah, et al. “Superfluid weight bounds from symmetry and quantum geometry in flat bands.” Physical review letters 128.8 (2022): 087002.
Regnault, Nicolas, and B. Andrei Bernevig. “Fractional chern insulator.” Physical Review X 1.2 (2011): 021014.
Liu, Tianhan, et al. “Fractional Chern insulators beyond Laughlin states.” Physical Review B 87.20 (2013): 205136.
Parameswaran, S. A., R. Roy, and Shivaji L. Sondhi. “Fractional Chern insulators and the W∞ algebra.” Physical Review B 85.24 (2012): 241308.
Lee, Jong Yeon, et al. “Emergent Multi-Flavor QED 3 at the Plateau Transition between Fractional Chern Insulators: Applications to Graphene Heterostructures.” Physical Review X 8.3 (2018): 031015.
Xie, Yonglong, et al. “Fractional Chern insulators in magic-angle twisted bilayer graphene.” Nature 600.7889 (2021): 439-443.
Spanton, Eric M., et al. “Observation of fractional Chern insulators in a van der Waals heterostructure.” Science 360.6384 (2018): 62-66.
Tian, Haidong, et al. “Evidence for Dirac flat band superconductivity enabled by quantum geometry.” Nature 614.7948 (2023): 440-444. (suspicious)
Xie, Fang, et al. “Topology-bounded superfluid weight in twisted bilayer graphene.” Physical review letters 124.16 (2020): 167002.
Julku, Aleksi, et al. “Superfluid weight and Berezinskii-Kosterlitz-Thouless transition temperature of twisted bilayer graphene.” Physical Review B 101.6 (2020): 060505.
Grushin, Adolfo G., et al. “Characterization and stability of a fermionic ν= 1/3 fractional Chern insulator.” Physical Review B 91.3 (2015): 035136.

Comment:

The Landau-Ginzburg-Nambu-Goldstone (LGNG) paradigm was once believed to potentially mark the culmination of solid-state physics. This paradigm revolves around the (continuous) symmetry of a Hamiltonian describing a system and how the ground state (or effective Hamiltonian) breaks that symmetry. Sometimes excitations (sometimes gapless) emerge to recover the broken symmetry. However, Walter Kohn’s discovery of a theory of the insulating state in 1964 raised doubts about whether there could be a paradigm beyond LGNG. Kohn found that the insulating state, regardless of the underlying mechanism (whether it be a band insulator, Mott insulator, Kondo insulator, Anderson insulator, excitonic insulator, etc.), exhibits a similar organization of the ground-state wavefunction. This organization, now known as the Fubini-Study metric of the wavefunction, allows for distinguishing between insulators and metals, including the characterization of metal-insulator phase transitions, extending beyond the LGNG paradigm. Unfortunately, the significance of Kohn’s paper was initially overlooked, which delayed the discovery of topological physics in condensed matter.

Following the groundbreaking discoveries of the quantum Hall effect and fractional quantum Hall effect, researchers began to grasp the importance of topology in condensed matter systems. The Landau levels exhibited intriguing properties, such as chiral fermions at zero energy and quenched kinetic energy. However, the key property behind the quantum Hall effect remained elusive until Thouless, Kohmoto, Nightingale, and den Nijs (TKNN) demonstrated that the integral of a geometric term from the ground-state wavefunction could be related to the Kubo formula for conductance. Subsequently, Simon realized that this property is characterized by a topological invariant, as known from Chern’s work.

To firmly establish topology as the key factor driving the quantum Hall effect, a clean model that solely relies on topological principles needed to be developed. Taking inspiration from anomaly flow in lattice gauge theory of Weyl fermions with U(1) gauge link variables, Haldane crafted a lattice model that achieved precisely that. The Haldane model not only allowed for a comprehensive understanding of the quantum Hall effect but also paved the way for the realization of the quantum anomalous Hall effect – a quantum Hall effect without Landau levels.

Once researchers gained a full grasp of the quantum Hall effect, they could systematically design different approaches to achieve it. One of the early successful experimental realizations of the quantum anomalous Hall effect was achieved by magnetically gapping out the surface gapless state in a 3D topological insulator, as demonstrated in the seminal work by Cuizu Chang and colleagues involving Cr-doped BST. Subsequently, this fascinating phenomenon was also realized in intrinsic magnetic topological insulators like MnBi2Te4 and symmetry-engineered twisted bilayer graphene.

This story highlights a valuable lesson – when we possess a deep understanding of a particular phase of matter, it becomes significantly easier to engineer and achieve that phase using different methodologies or experimental routines.

Indeed, fractional quantum anomalous effect, a lattice version of the fractional quantum Hall effect, remains an intriguing and challenging phenomenon to fully comprehend and engineer. While there are some theoretical insights into this phase, its experimental realization has proven to be non-trivial. The role of flat quantum geometry is suspected to be crucial in understanding this intriguing behavior. Our (Xiaodong Xu lab at University of Washington) recent discovery of this phase in twisted MoTe2 holds great promise in accelerating our understanding of this elusive phase through experimental investigations.

Flatband superconductors present another captivating avenue of research, but there is still much to uncover and comprehend. The realization that kinetic energy quenching can affect the formation of superconductivity, with the superfluid weight being bounded by quantum metric rather than the Hamiltonian, opens up new perspectives in this area. Nonetheless, solid experimental evidence is crucial to draw concrete conclusions. I highly recommend a systematic numeric investigation and propose the use of an ultracold atom simulator to explore this intriguing phenomenon further.

It’s clear that there is a long and fascinating story to be told about these subjects, which could potentially form the next chapter in the field of condensed matter physics. As you delve into more in-depth discussions, step by step, we can look forward to unraveling the mysteries of these exotic phases and their implications for the broader field of physics.

Highlighted note:
https://zhuanlan.zhihu.com/p/629260535 ( Unfortunately it is in Chinese. I heard he is to be a master student in Weizmann, and will seek phd oppotunity. Interested one can ask me for contact info of him. )

Topic. 2 The Onsager’s relation (Feb. 27)

References:
Wikipedia: https://en.wikipedia.org/wiki/Onsager_reciprocal_relations
Papaj, Michał, and Liang Fu. “Magnus hall effect.” Physical review letters 123.21 (2019): 216802.
Böttcher, Jan, et al. “Survival of the quantum anomalous Hall effect in orbital magnetic fields as a consequence of the parity anomaly.” Physical Review Letters 123.22 (2019): 226602.
Kimura, Takashi, et al. “Room-temperature reversible spin Hall effect.” Physical review letters 98.15 (2007): 156601.
Cao, Helin, et al. “Photo-Nernst current in graphene.” Nature Physics 12.3 (2016): 236-239.
Ma, Qiong, et al. “Photocurrent as a multiphysics diagnostic of quantum materials.” Nature Reviews Physics 5.3 (2023): 170-184.

Comment:

The Onsager reciprocal relation stands as a fundamental principle applicable to various transport phenomena. Although typically valid, its violation can be intriguingly nontrivial in cases like Ferromagnetic hysteresis. Nevertheless, the reciprocal principle formulated by Onsager proves useful in accurately deriving transport coefficients from imperfect experimental data. Moreover, the generalization of the Onsager relation to address Ferromagnetic hysteresis involves considering separate conservations during the processes of sweeping up and sweeping down the magnetic field. This, however, gives rise to a profound question: what represents the most generalizable form of the Onsager relation? If we extend the Onsager relation to the microscopic level, could it potentially serve as a more fundamental law than the concept of conserved current?

Topic. 1 The Anderson’s Orthogonality Catastrophe (Feb. 20)
References:
Infrared Catastrophe in Fermi Gases with Local Scattering Potentials, P. W. Anderson, Phys. Rev. Lett. 18, 1049
Latta, C., Haupt, F., Hanl, M. et al. Quantum quench of Kondo correlations in optical absorption. Nature 474, 627–630 (2011). https://doi.org/10.1038/nature10204

Comment:

In 1967, Anderson made a discovery while investigating the perturbation (or scattering) of a sudden potential acting on a many-body wavefunction in its ground state. He observed a counterintuitive phenomenon wherein the overlap between the scattered state and the ground state tends to vanish as the system approaches the thermodynamic limit ( $N \to \infty$ ). This finding has provided crucial insights into various experimental phenomena, particularly in spectroscopy. Notably, it has shed light on perplexing occurrences like the X-ray absorption anomaly (commonly known as the X-ray edge problem and Fermi singularity) and the enigmatic Kondo problem.

Note:
https://junkaidong.github.io/physics/orthogonalitycatastrophe/. Junkai Dong is a graduate student in Ashvin’s group at Harvard. He reviewed an intuitive version of derivation and pointed out many interesting related aspects.

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