In many-body quantum systems at ultra‑low temperatures, the collective behavior of particles can give rise to exotic states of matter such as superfluids and quantum liquids. These states exhibit macroscopic quantum coherence and support topological excitations, yet their internal mechanical response has traditionally been described only by local thermodynamic variables such as pressure, density, and temperature. In this work we introduce the concept of a topological pressure field, denoted \(P_T(x)\), which captures the influence of non‑trivial topological order on the local mechanical pressure within a quantum liquid. The proposed field is derived from a gauge‑invariant formulation of the quantum stress tensor that incorporates Berry curvature and Chern‑Simons terms. We show that \(P_T(x)\) is non‑zero only in regions where the quantum state hosts topological defects such as quantized vortices or skyrmion‑like textures. Using a simplified model of a two‑dimensional superfluid film, we calculate the spatial profile of \(P_T(x)\) around a vortex core and predict measurable deviations from the classical pressure distribution. The existence of \(P_T(x)\) implies that quantum liquids possess an additional mechanical degree of freedom that is purely topological. This insight opens a pathway to experimentally detect topological pressure via precision pressure sensors in superfluid helium or cold‑atom Bose‑Einstein condensates, and suggests new avenues for engineering quantum fluid devices that exploit topological mechanics.
In many-body quantum systems at ultra‑low temperatures, the collective behavior of particles can give rise to exotic states of matter such as superfluids and quantum liquids. These states exhibit macroscopic quantum coherence and support topological excitations, yet their internal mechanical response has traditionally been described only by local thermodynamic variables such as pressure, density, and temperature. In this work we introduce the concept of a topological pressure field, denoted (P_T(x)), which captures the influence of non‑trivial topological order on the local mechanical pressure within a quantum liquid. The proposed field is derived from a gauge‑invariant formulation of the quantum stress tensor that incorporates Berry curvature and Chern‑Simons terms. We show that (P_T(x)) is non‑zero only in regions where the quantum state hosts topological defects such as quantized vortices or skyrmion‑like textures. Using a simplified model of a two‑dimensional superfluid film, we calculate the spatial profile of (P_T(x)) around a vortex core and predict measurable deviations from the classical pressure distribution. The existence of (P_T(x)) implies that quantum liquids possess an additional mechanical degree of freedom that is purely topological. This insight opens a pathway to experimentally detect topological pressure via precision pressure sensors in superfluid helium or cold‑atom Bose‑Einstein condensates, and suggests new avenues for engineering quantum fluid devices that exploit topological mechanics.
The concept of pressure in quantum fluids has traditionally been treated as a static scalar quantity derived from macroscopic equations of state. In this work we introduce a dynamic, frequency-resolved pressure field P(ω) that captures the intrinsic oscillatory stresses within a quantum liquid. This Quantum Liquid Pressure Spectrum (QLPS) framework derives from the fundamental commutation relations of the field operators and the continuity equation for mass and momentum. We present a systematic derivation of P(ω), illustrate its dependence on the excitation spectrum, and discuss its implications for superfluid helium, ultracold Fermi gases, and potential applications in quantum sensing and precision metrology. The QLPS concept reveals a previously inaccessible quantum variable that may provide a new handle on the collective excitations and phase transitions in strongly correlated quantum fluids, offering a pathway toward novel quantum technologies and a deeper understanding of quantum many-body physics.
The concept of pressure in quantum fluids has traditionally been treated as a static scalar quantity derived from macroscopic equations of state. In this work we introduce a dynamic, frequency-resolved pressure field P(ω) that captures the intrinsic oscillatory stresses within a quantum liquid. This Quantum Liquid Pressure Spectrum (QLPS) framework derives from the fundamental commutation relations of the field operators and the continuity equation for mass and momentum. We present a systematic derivation of P(ω), illustrate its dependence on the excitation spectrum, and discuss its implications for superfluid helium, ultracold Fermi gases, and potential applications in quantum sensing and precision metrology. The QLPS concept reveals a previously inaccessible quantum variable that may provide a new handle on the collective excitations and phase transitions in strongly correlated quantum fluids, offering a pathway toward novel quantum technologies and a deeper understanding of quantum many-body physics.
In strongly correlated quantum liquids, topological and local defects can give rise to emergent excitations that are neither conventional phonons nor magnons. We introduce the concept of Quantum Liquid Defect Quasiparticles (QLDQ), a class of collective modes generated by the interplay of quantum fluctuations and structural imperfections. These quasiparticles, denoted Dq, possess dispersion relations that mirror those of phonons but arise from the defect core rather than lattice vibrations. Using a field‑theoretical approach, we derive the effective action for a defected quantum liquid, identify the spectrum of Dq modes, and analyze their statistical, topological, and thermodynamic signatures. We discuss how the presence of Dq modifies the low‑temperature behavior of superfluid systems and outline potential routes to detect them in ultracold atom experiments and low‑temperature condensed‑matter platforms. The discovery of QLDQ would open a new avenue for exploring elementary excitations in quantum fluids and may have implications for quantum technologies that exploit defect‑based coherence.
Since the discovery of Bose-Einstein condensation in dilute atomic vapours in 1995, there has been a monumental increase in the research effort in the field of atomic physics due to the unforeseen opportunities and challenges that the degenerate quantum gases present. In particular, quantum gases can emulate complicated models that arise in solid state and high energy physics, allowing realisations of exotic phenomena that have proven to be elusive in their original context. An outstanding example is the existence of various topological defects in degenerate quantum gases with internal degrees of freedom. Topological excitations such as skyrmions and several types of monopoles can be shown to take place in Bose gases with a hyperfine spin degree of freedom as a result of a coupling to an external field or due to thermal fluctuations. A central question in the context of dilute Bose gases is the relation between superfluidity and Bose-Einstein condensation. The dimensionality of the underlying space as well as the internal degrees of freedom have a direct impact on the existence and the nature of the Bose-Einstein condensate. For example, any uniform Bose gas in two spatial dimensions or an antiferromagnetic spinor Bose gas can give rise to a superfluid state which does not involve a conventional Bose-Einstein condensate corresponding to a single macroscopically occupied quantum state. In this Thesis, properties of different topological defects and their relation to superfluidity in dilute Bose gases are investigated. Stability and creation of coreless vortices are first studied and a method to cyclically increase the angular momentum of the condensate is introduced. Subsequently, the properties and creation of different types of monopoles are investigated and an experimentally feasible method to create a Dirac monopole is presented. Finally, finite temperature phase transitions in quasi-two-dimensional Bose gases with a spin degree of freedom are analysed and, as a related subject, the stability of vortex clusters formed by vortices and antivortices is studied.
Topological phases of matter are purely quantum mechanical and have no classical analogue. Most phases in nature can be classified and studied classically through the concept of symmetry breaking and its theoretical description, Landau-Ginzburg field theory. In contrast to the general wisdom of Landau-Ginzburg field theory, the topological phases share the same symmetry as a trivial insulator and still are different phases. Having gapped spectrum in bulk, they support a metallic edge excition robust against symmetry-respecting perturbation or an emergent fractional excitation in bulk. Following after fractional quantum Hall fluids, many topologically orderd phases, such as spin liquids and topological insulators, have been found and studied. Spin liquids are disordered phases of frustrated antiferromagnets and do not freeze and order even at the lowest temperature. They support an electrically neutral spin-1/2 excitation, which does not exist in a microscopic scale, with emergent dynamical gauge field in bulk and do not have an adiabatic path to a trivial paramagnet phase. The topological insulators are time-reversal symmetric band insulators which cannot evolve smoothly into a trivial insulator with the symmetry, and they have been intensely studied theoretically and experimetally for the last decade. Though the topological insulators are inherently non-interacting systems, they have exotic gapless edge and surface states which demonstrate many interesting quantum phenomena such as fractionalization, axionic electromagnetism, and half quantum Hall effect. In this thesis, we study various quantum phenomena of the topological phases, mainly of the topological insulator and its close relatives in which the physics of spin liquids has been merged into. As they are intrinsically quantum many-body states, the quantum field theory is an invaluable tool to explore the venue of the phases and will be used thorougly in this work. First, we present a topological field theoretic description of the topological insulators and translational symmetric Z2 spin liquid. We demostrate that abelian BF theory is an effective field theory for the two and three dimensional topological insulators. We show that the phenomenologies of BF theory are consistent with those of the topological insulators such as gapless edge and surface excitations and response functions to external gauge field. The same form of the BF theory is also applicable to study the certain classes of Z2 spin liquids with the gapless edge states. We closely examine the possible gapless edge theory of the BF theory and the translational symmetric spin liquids, and we show that the effective BF theories capture the bulk properties as well as the gapless edge spectrum of the spin liquid. Also we discuss the zero-temperature phase diagram of a thin film three dimensional topological insulators with two competing mass terms: time-reversal symmetric exciton condensation and time-reversal symmetry breaking Zeeman effect. There are two phases, quantum spin Hall phase and quantum anomalous Hall phase, and both phases support fractional excitations. We derive an effective topological field theory for the fractional excitations and examine the origin of the fractional excitations. Next we consider the relatives of the topological insulators. First we discuss the proximate symmetry broken phases of topological Mott insulator, a U(1) spin liquid with fermionic spinons in the topological insulator state. The topologically non-trivial band structure of the spinon generates the axion term for the gauge field, and we show that the axion term changes the nature of the confined phase of the spin liquid. Contrast to the conventional confined phase which has only a bond order, the confined phase of the spin liquid is in general a coexisting phase of the two different orders : a current order and a bond order. We then consider another relative of the topological insulator: a bosonic symmetry protected topological phase in two dimensional space, with both PSU(N) and time reversal symmetry. We develop an effective field theory for the phase, which is a SU(N) principal chiral model with a theta-term, and reveal the physics of the topological phase in detail.Finally we consider a topological semimetal, namely a Weyl semimetal. We first demonstrate that the Weyl semimetal can be realized in the magnetically doped topological band insulators. We explicitly derive the low energy theory of Weyl points from the general continuum Hamiltonian and tight-binding model of the topological insulators. Then we study superconducting instabilities of doped Weyl semimetals. We consider a minimal model for a Weyl semimetal and study the superconducting instabilities induced by a short-ranged attractive interaction. With the interaction, we find two competing states: a fully gapped finite-momentum pairing state and a nodal even-parity pairing state. We show that, in a mean field approximateion, the finite-momentum pairing state wins energetically against the usual even-parity paired state. We also show that exotic modes are localized at the full and half quantum vortices of the finite-momentum pairing state.
Topological quantum phases of matter are often characterized by the presence of fractionalized quasiparticles, which exhibit non-trivial braiding statistics or carry fractional quantum numbers, or of protected gapless surface states. In this thesis, we study topological phases in two and three spatial dimensions, from the perspective of searching for new exotic quantum phases and of characterizing their experimental signatures.\nWe first study topological defects in fermionic paired superfluids and discover that in the presence of a multiply quantized vortex, such a state hosts unpaired fermions in the BCS regime. We predict that these unpaired fermions will result in an experimentally measurable deviation of the system's angular momentum from its value in the BEC regime. Focusing on two-dimensions, we then study superconductors coupled to dynamically fluctuating electromagnetism, and establish a universal framework for studying the low-energy physics of such systems. We derive topological field theories describing all spin-singlet superconductors which naturally capture the interplay of symmetry and topology in these gapped states.\nThe remainder of this thesis is focused on a novel class of long-range entangled states of matter, known as “fracton” phases, in both two- and three-dimensions. These phases exhibit an intriguing phenomenology, most surprising of which is the presence of excitations which are immobile in isolation. Studying the non-equilibrium dynamics of gapped fracton phases, we discover that they naturally exhibit glassy quantum dynamics in the absence of quenched disorder, and hence may have potential technological applications as robust quantum memories. Finally, we conclude with a description of fracton phases as higher-rank tensor gauge theories and discuss the emergent phases of matter in which a finite density of fractons or their bound states may exist.